I guess it depends on the jurisdiction.

I can tell you that here in Switzerland, in principle, there is no difference between murder and attempted murder when it comes to sentencing.

In the end, it all boils down to the reason why it remained just an attempt, and we differentiate different types of attempts. Particularly, an attempt can be completete or incomplete, and furthermore it can be failed or inadequate.

Say, for example, the felon waited for you in the house, with the intention to kill and the rob you, shot you in the face, then left you for dead - and still, by some huge stroke of luck you survived. The sentencing would not be impacted by your survival. He meant to murder you, and all he did would have normally sufficed to reach his goal. The attempt was completed and the used method adequate.

On the other hand, if the same felon in the end just shoots you in the foot once, not because he missed (inadequate attempt) or refrains from shooting at all (attempt not completed), or he shoots you in a way that could actually kill you if left alone but he immediately regrets it, tends to your wound and calls an ambulance, and you survive (attempt completed with immediate and true remorse)... well, it's understandable that this won't and should not be sentenced the same as a cold blooded murder.

To add to the existing arguments, consider this from the point of view of crime deterrence, i.e., you view the sentence as a means to deter people from murdering others.

Specifically, suppose that Alice attempted to murder Bob but failed. If Bob has noticed, Alice is confronted with the risk that he secures evidence, alerts the authorities, and eventually she gets sentenced for attempted murder. In many situations, the most feasible way for Alice to avoid this is to murder Bob. For example if Alice tried to shoot Bob and missed, her best option to avoid a sentence is often to try to shoot Bob again. Now, in a system where the sentence for murder is the same as for attempted murder, there is no legal incentive for Alice to not attempt to murder Bob again: The worst that can come from murdering Bob is the same sentence she would be facing for attempted murder, while at best a successful murder allows her to cover up her crime. This is obviously bad for Bob.

In general, this is one reason to sort the punishments of crime by severity as far as possible. For example, if the punishment for theft is the same as for robbery, there is no incentive for the thief not to use violence if caught in the act. Or, if the punishment for rape is the same as for murder, there is no legal incentive for a rapist not to murder his victim to cover his tracks.

Other answers list quite valid points, but miss the following one:

No penal system is perfect.

A reasonable system would account for its own imperfections.

A murder is quite easier to prove than an attempted murder.

Why is ...

Not sure about US/UK laws, but based on German laws, this question is a highly opinion-based question so my answer will be opinion-based.

I also have to say that I'm not a lawyer, so my answer is not an expert's answer.

Why is murder considered a more serious crime than attempted murder?

Background

German law (§23 StGB) states that ...

• ... an attempted crime "can" be punished less hard than the "successful" (*) crime; however, the word "can" means that it is also possible to punish the attempt as hard as the "successful" crime.
• ... an attempted crime may even be left unpunished if the success was absolutely impossible from the beginning. For example if somebody tries to stab another person with a gun instead of a knife.

I know that German courts do punish less hard if the criminal made mistakes and therefore the crime was not successful. They would punish an attempted murder the same way a murder is punished if the murderer did everything "correctly" and it is not the murderer's "fault" that the victim is still alive.

My personal interpretion of this rule is:

The fact that a murder "failed" because the murderer made stupid mistakes is an indication that the murderer did not really want to commit the murder.

Therefore, the attempted murder is punished less hard.

However, if there are no signs that the murderer did not really want to commit the murder, the attempted murder is punished the same way as "successful" murder.

And "same punishment" also means that the attempted murder is not seen as less serious than successful murder.

(*) German law really uses the word "successful" here.

In response to the comment that Wrzlprmft wrote below about no incentive to stop attempting to murder a person, I'm not sure I agree about that. For one thing, possibly every time an attempt is made, an additional element of risk is introduced into the would-be-murderers life, whether or not the attempt is successful. I would argue most crimes are of this nature. Whether or not you actually sell some drugs, offering them on the street is bound to be risky. The same with prostitution, spousal abuse, and probably even terrorism. (Even if your bomb is a dud, placing it in the Embassy is risky...) So your incentive for not trying to murder a person again is that you are less likely to get caught. Am I missing something there?

I can imagine situations where a person has an uncertain amount of planning and intent to commit a crime. We aren't robots... well, maybe we are; that is to say our actions are determined by the laws of chemistry/quantum mechanics- just like robots and computers. But we ourselves have insufficient introspective power to know how we will act on particular contingencies.

My father was murdered in Costa Rica about a decade ago; and for a long time I tried to hunt the killer down with the intent to commit retributive violence on him. The townspeople were of very little help, and the trail got cold fast despite my offer of a $8K cash reward for information. (All I could scrape together at the time.) All this time, while I did more than occasionally fantasize about "making him pay", another line of thought became dominant where I merely demanded to know why he killed my father, who was reading a book under a tree when his killer snuck up and shot him in the back of the head. (This according to the OIJ, eg the Costa Rican FBI.) So my "plans" were largely unformed, and hinged on further information about the killer. Maybe my father threatened to assault them or their family. (Super unlikely- he was an incredibly shy and introspective musician.) Because I was unable to assess the motive, I didn't know how I would react emotionally to a confrontation with the killer if it was to occur. They didn't even take anything from his backpack after killing him- so theft probably wasn't on the menu.

I think most murders aren't cold-blooded (eg pre-meditated) but are rather crimes of passion. Sort of like road-rage. An already unhinged gun nut (I mean owner), when beaten up at a bar for cheering for the wrong soccer team, might drunkenly return with their firearm to "make them pay". And similarly to myself; they might not even know what "making them pay" entails. It is pretty disheartening thinking "some people with guns just like to kill other people for no particular motive other than it being as easy as point-and-click" - but that seems to be the most likely scenario. At least with knives or fists, there is more effort required to kill a person; and I think possibly in the middle of beating a guy up a possible killer might think "this is pretty hardcore. Maybe he learned his lesson already" - even if their intent was originally to punch the guy to death.

For this reason I think success should be a major part of the sentencing system. Many of the posts here seem to indicate a little bit of .. well, philosophical abstraction from the realities of planning/thinking about a thing versus actually doing it.

How broadly can you define "attempted"?

If a murder is successful, there is certainty that the punishments are warranted given the crime.

But what counts as "attempted" will always require a degree of interpretation both of actions and intent. A lighter punishment concedes this uncertainty.

Rhetorically, should those accused of attempted murder be eligible for the death penalty? Given that the death penalty already has uncertainty associated with wrongful convictions, introducing greater uncertainty by applying it to people who have not actually murdered a person seems unwise.

The legal theories regarding homicides have changed a lot, but there has not always been some kind of distinction between the attempt and the result. It's the distinction between an assault with a deadly instrument and the resulting killing. And not all jurisdictions look at things the same way! The aspect of killings under the aspect of Law in History is a very interesting question:

Republican Roman Law dictated to torture all slaves of a killed landowner to find out if any of the slaves were in league with the killer because Law dictated slaves were needed to be tortured so their testimonial was admissible in court. And then, all that were found to have not protected their owner could be summarily executed¹. The very same state also said that not all killings were equal: Killing your own father or close relative was seen as more heinous and was punished by a more cruel death than killing your neighbor while inflicting death upon your own slave was without punishment, slaying someone's else slave was a civil dispute where you destroyed a thing.¹ But Roman law did not have murder per se, only homicide, which was defined by the intent and the item used - it didn't matter if you did succeed at once, or if he died later from the wound:

On the other hand the Roman law had but one crime of this nature, viz., homicidium (with its aggravated form of parridicium or slaying of a relative) and this originally .was purely a crime of intent.¹⁵_{Hunter, Roman Law, 1069} Thus, fatally wounding another with a sword was homicidium; but striking him with an .iron key was not, even though the result should prove equally fatal. ¹⁶_{Justinian's Digesta, XLVIII, VIII, I, III.}

Negligence resulting in death is mentioned as early as the Twelve Tables, but not as a crime, nor was it visited with a serious penalty. "One who slays another accidentally," it is declared, ¹⁹_{XII Tables, VIII, 24} "shall provide a ram to be sacrificed in his stead." ²

The same document quoted here also shows some insight in other areas where the distinction between different types of killings comes from, for example in Japan:

Chapter XXVI of the Japanese Penal Code treats of (intentional) homicide which may be given capital punishment.³⁷_{Japanese Penal Code, Art. 199.} But Chapter XXVIII covers "involuntary (accidental) homicide" which is "punished with a fine not exceeding one thousand yen."³⁸_{ld. .Art 210.}

This refers to the Japanese Penal Code, which also lists in the 1960 edition:

Article 199　A person who kills another shall be punished by the death penalty or imprisonment with work for life or for a definite term of not less than 5 years.

Article 201　A person who prepares for the commission of a crime prescribed under Article 199 shall be punished by imprisonment with work for not more than 2 years; provided, however, that the person may be exculpated in light of circumstances.

Article 202　A person who induces or aids another to commit suicide, or kills another at the other's request or with other's consent, shall be punished by imprisonment with or without work for not less than 6 months but not more than 7 years.

Article 203　An attempt of the crimes prescribed under Article 199 and the preceding Article shall be punished.

Here we see that murder is not defined. Just "you kills somebody, you get punished" under 199, 201, 202, or 203. Attempt here is apparently punished just like the deed itself, even preparing a killing is a crime.

A totally different approach has modern Germany under StGB 211, prescribing always life in prison as the sentence for the done deed. As it is a Verbrechen to commit murder, the StGB 22 does make it's attempt punishable, in principle also with the same punishment. However, the judge can use StGB 23 Abs. 2 to lessen the punishment to 3-15 years as StGB 49 dictates, and total incompetence (like... attempting to stab somebody to death with a rubber knife held between the teeth while having the feet tied together) can allow to not punish at all or any other lesser sentence under StGB 23 Abs 3. But Germany also has a single article in its Grundgesetz, which carves out a hole in the normal laws:

(4) Gegen jeden, der es unternimmt, diese Ordnung zu beseitigen, haben alle Deutschen das Recht zum Widerstand, wenn andere Abhilfe nicht möglich ist.

(4) All Germans shall have the right to resist any person seeking to abolish this constitutional order if no other remedy is available

This has been discussed as possibly including a carte blanche to murder of a dictator, but so far hasn't been invoke ever.

You may get more effective murderers that way

I would frame the question from the perspective from the criminal.

If they know they will be punished equally from attempted murder from actual murder, they will try harder to get the results they want. More if is this common knowledge.

By rewarding incompetence, you may end with a incompetent murder instead of a competent one. It probably easy to rehabilitate the former.

Your question is the subject of longstanding and ongoing debate that has generated countless articles and books and dissertations, so you're probably not going to get a fully satisfactory answer here.

But here's the short version: Different systems operate on different assumptions. Your question suggests you are not a retributivist, i.e., someone who view sentencing as a means for taking retribution for the criminal's offenses. Some systems (most, I imagine) are built around that idea, but some view criminal sentencing primarily as a means of preventing recidivism, or as a means for achieving rehabilitation, the interests you indicated you see as more important.

And even within those systems, there are still different ideas about what you're actually trying to do. Again, you've indicated that you subscribe to an intent-based system (a punishment keyed to what the criminal intended to do), but that approach competes with harm-based sentencing (punishment for the harm the criminal actually caused).

While equal punishments make sense from an intent-based approach, they are less justifiable from a harm-based approach. Few would say that attempted murder inflicts the same amount of harm as completed murder, and so that system does not call for the same amount of punishment.

Because there are different approaches, sentencing guidelines vary from jurisdiction to jurisdiction. The U.S. Federal Sentencing Guidelines, which I would classify as adopting a harm-based retributivism, treat attempts less severely than completed offenses, but other systems treat them equally.