Others basically said it all. Small recommendarion though - you can't really get acoustic sound from normal pickups - if you're after that, try to find some guitar with piezo pickup. They're usually built-in in the bridge.

It depends on guitars. But it is all about sacrificing. if you want acoustic like sound, you want piezo not single coil but cheapest bridge + all required electronics costs 300-400 USD

HSH examples

FRM150 (Paul Gibert's guitar) is wired in way he gets all humbucker combinations neck, bridge, neck+bridge, bridge+middle, neck+middle. This is hard to call Les Paul due to master volume/tone control but covers all entry level HH guitars. He sacrificed all real single coil sounds and left only two strat sounds.

JEM77 (Steve Vai's guitar) is more classic. He sacrificed bridge + neck for having real single coil sound in middle. For some players having real single is priceless for someone is just a gadget. But this wiring is older and more popular.

HH examples

The most known is three position switch with bridge, both, neck. Some, for example Les Paul, have separate volume/tone that will be missing in HSH. Some have split or tap or can be running in parallel.

S521 all humbucker combinations, neck + bridge split/tapped and bridge in paralel. Parallel humbucker is something like strat sound but coils are much closer.

JP6 - Piezo (John Petrucci's Guitar) is being sold as HH but has bridge with piezo pickup. Piezo gives acoustic sound, that would make me more happy than single coil if could afford, and it can be combined with humbuckers.

The sound

Some manufacturers offer different humbuckers for 250K volume pot equipped guitars. Sound of split single coil also varies by specific models. Some handle it better than others.

Conclusion

You can simulate any sound of three pickup guitar with two pickup guitar and vice versa, the only problem is getting it with proper wiring or customizing it. Even they will not sound the same may be close enough for your application or even better. And don't forget about potentiometers problem. The 250K potentiometer will cut some frequencies from humbuckers while 500K make singles brighter than they are by default. It may be not a problem or critical to choosing favorite tone :D

Dont forget that the magnetic attraction of the pickup poles simply being present will affect the string vibration and tend to kill harmonics the more pickups/coils are present. That's why EVH stripped his guitar to just bridge HB.

The short answer is that an HSH guitar can be wired to do everything an HH guitar can, but provides the additional option of mixing in the middle single coil.

HH guitars are usually wired with a three-way switch (neck, middle, bridge) and either master volume and tone or individual pickup volume and tone.

As standard, HSH guitars are usually wired with a five-way switch (neck, neck+middle, middle, middle+bridge, bridge). This gives you two of the three HH tones, but misses out the neck+bridge double-humbucker tone.

However, it is possible to alter this - for example, you could have an HSH with the standard HH three-way switch and a separate switch or volume control to add the middle pickup to any position - this now gives two additional options over the five-way (neck+bridge and neck+middle+bridge).

And all of that is without considering the various coil-tapping options; on some HSH guitars, one or both of the mix positions are sometimes wired with an automatic coil tap, so e.g. neck+middle would be only one coil of the neck pickup mixed with the single-coil middle pickup.

Basically, if you can wield a soldering iron (or get someone to do it for you), the world's your oyster!

Time was, Fender Stratocasters used a three-position switch, corresponding to neck, middle and bridge pickups. Granted, single-coil, so just bear with me.

Players discovered that, if you put the switch in the right position, you could get the neck-and-middle and bridge-and-middle sounds. Jimi Hendrix is a popularizer of this technique, and it became popular enough that the Strat got wired stock with five-position switches. Eventually the middle pickup was made reverse wound and reversed polarity, so that neck-middle and bridge middle would effectively be noiseless, humbucking positions.

When Ibanez came to Steve Vai about making a signature guitar for him, he said he wanted to get those positions and tones with neck and bridge humbuckers, with coils tapped so you'd get one coil of the neck or bridge with the single coil in the middle, so it's a hum-less Strat setup. This is what you cannot get with H-H setup.

As the H-S-H wiring is usually a variation on Strat wiring, you generally get the middle pickup in middle position, while H-H guitars generally have neck-bridge as the middle position. It is doable to set the circuit so that the middle position is neck-bridge, but generally, you have it in H-H guitars and not H-S-H guitars.

Either way, H-S-H guitars are generally master volume and master tone, while Les Paul-style H-H guitars have separate volume and tone. With Les Pauls, you can set, for example, the neck volume to zero, so the switch becomes bridge-bridge-none, making it a kill switch. This is not available with a H-S-H Vai-style guitar.

EDITED FOR CLARIFICATION

If someone doesn't know what they want thier guitar to do, they should always get HSH. I'd certainly say it's the most versatile set up. Given the usual wiring (5 way switch) with switch position 1 being the neck pickup and 5 being the bridge, HSH gives a great deal of tonal variety.

For my tastes, position 1 on a clean tone can be a bit too boomy. Even if one backs the volume a bit to take the edge off, it doesn't quite suit acoustic-style strumming. Position 2 is perfect for these sorts of things, though. I'd always use it for the small high chords you often find in funk and reggae. Position 2 is also a nice way thinning a distorted tone without it cleaning up too much, like Position 1 with the volume dialled down does. If you have your rig set so Position 1 screams, Position 2 will sing.

The middle S (Position 3) by itself also works very well for chord strumming, and it also responds very well if slapping is something you like to do (A single coil in the middle is literally the textbook choice: Single coils typically have more bite and will bring life to the pops, and it's position will ensure the slaps aren't too boomy (like a neck pickup would be) or too tinny/nasally (like a bridge pickup would be)).

I don't use Position 4 very much, but that's because I think it has a rather specific sound I don't want very much. With a tiny bit of gain, this would be the position I would play the synth parts of Stevie Wonder's "Superstition" with. It would be perfect for bassier funk riffs in that sort of vein.

In general, the typical situation is that HSH gives me options of cleaner/thinner/clearer tones which aren't as achievable with HH (even with volume and tone pots in use!). These are options I use very frequently, and I'd feel pretty restricted with HH! Though of course, this isn't the case for everyone. Indeed, I'm quite fascinated at the variety of tones Ron Thal and Andy Timmons get from the overly-simple SH set up they prefer!

You will surely not be able to play a strong single coil in the H-H guitar. You could tap a 4-wire humbucker for a single coil sound, but in my experience the tapped humbucker doesn't sound as "warm" as a separate single coil. I too wanted the best of both worlds and I took the following approach.

Keep in mind that there are further differences in the traditional humbucking and single coil setups, such as pots and caps.

1. Humbuckers generally use 500K pots, single coils generally use 250K pots. Metal players may use 1M pots for humbuckers.
2. IIRC, humbuckers often use 0.047 capacitors. Single coils halve that to a 0.022 cap. Of course, vari-tones and similar mods provide a selection of caps on board.

In my own (first) project guitar, I did not know quite what to expect, so I built it with HSH pickups and two complete signal paths. The humbucking path uses 500k pots and an 0.047 cap; the single coil path uses 250K pots and a 0.022 cap. I did this with stacked, concentric CTS 250K/500K pots and an on/on toggle switch, all within the minimal confines of a standard Telecaster control plate. I created a custom 5-way selector switch to isolate the single-coil wiring from the humbucking combinations, but in the end when I flip the switch I opted for just the stand-alone single coil for the warmest sound. As I said above, the tapped humbuckers just didn't compare. This project is a work in progress; I hope this helps you find your own path.

Even with a H-H configuration, you could utilize coil splitting to achieve single coil-ish sounds. While arguably this does not give a "true" single coil sound, if humbucker sounds are mainly used, this can be enough. My impression is that most people aren't using the middle position that much, I think the way forward is to try different pickup configurations to find out what you need.

A lot of, if not most, blues players use humbuckers, so a good blues tone is definitely achieveable.