Why are these film photos brighter than digital photos taken at the same time with the same settings?

They could simply not have the scanner calibrated, or they have some arbitrary values.

You need to analize the negative and check if it is really that overexposed.

But also take into account that even between film manufacturers the look has diferent results.

The digital camera has a higher dynamic range than the film; as a result, film will not be able to show the bright and the dark areas with the same details as the digital camera.

In this case, you lost the details in the bright areas, they have started to burn out.

If the development would have been done slightly darker, the brighter areas would look pretty much identical in both shots, but the dark areas would have lost all detail (and would look evenly black).

If you know what HDR is - film basically does a LDR, a lower-dynamic range. I cannot provide the correct numbers, but for comparison, assume that film has 10 steps dynamic range, a cheap digital camera 10-12, and a professional digital camera 12-14. HDRs have more than that, typically up to 20, but theoretically unlimited, as they are processed from multiple (any number of) shots. The human eye has about 18 steps (which is why we have no difficulty seeing a night scene with bright lights and dark corners). Considering the adaption of the iris, the total range for the human eye is over 40 steps. [I read those numbers a long time ago and my memory might be wrong, but they still illustrate the concept]

There is some latitude with regard to ISO sensitivity. Digital cameras often are less sensitive than the rated "base" sensitivity. The manufacturers tend to round up, possibly because it can make test results look better than they actually are. It also helps to preserve detail in the highlights. With film the manufacturers tend to round the sensitivity down.

With either film or digital the response curve from the darkest to lightest details to which the camera is sensitive can vary from one camera (digital) or film to the next. Even if the midtones are exposed identically, the highlights may be brighter or darker from one film to the next or from one digital camera to the next. The same is true for the shadows.

Then there's the whole reciprocity error (Schwarzschild effect) thing with film when exposing for longer than about one second.

Unless the exposure times were long enough that the Schwarzschild effect comes into play (and your recent comment indicates they weren't), your specific case to me seems to most likely be due to overexposure of the film when shot or over development of the film. The reason the digital images are not also overexposed may be due, in part, the lower sensitivity of the digital camera at the same ISO setting but is probably most influenced by a processing algorithm such as Canon's Auto Lighting Optimizer or an Auto setting in the profile used by Adobe Camera Raw that alters the gamma curves when converting the raw data based on the content of the scene.

To be more specific regarding the case of the example photos in the question: ACR ignores most of the "maker notes" section of the EXIF data that save the in-camera settings at the time the photo was taken. When you opened the raw files in ACR the default profile ACR used to interpret the data in the raw files likely applied some automatic adjustments to prevent displaying the brightest values in the raw data as blown highlights. It likely did the digital equivalent of reducing the development time of the analog negative to prevent blowing the highlights. But your analog negatives were developed without such a consideration for the overexposed highlights.

Had you opened the same raw files in Canon's Digital Photo Professional with the Neutral picture style applied, Auto Lighting Optimizer disabled, and everything else (brightness, contrast, highlights, shadow, etc.) set to "0" you would probably have gotten results much closer to what the film lab gave you than you did using ACR with an unknown profile applied.

Remember, there is almost always more information in a raw image file than can be displayed on an 8-bit monitor. This is particularly the case with images of high dynamic range scenes. So when you open a raw file in ACR, or any other application that displays an image from the data in a raw file, what you see on the screen is only one interpretation of that data. You're not actually looking at the data itself.

Film is not brighter, it has different tone curve. In your examples highlights and shadows from negative are translated differently to the print than digital.

With traditional films like the HP5 the curve is S-shaped. Also, with the black and white example, each film has certain tonal response to different colors, your digital conversion to bw has a different one. This may cause difference in skin tones, for example.

If you want to get digital results that are closer to film, use some of the film emulating bw conversion plugins like Silver Effex.

It is also possible that the films came from the lab a bit overdeveloped.

There is the potential for variations in many of these steps, but the first one that jumps out at me is that you used the same ISO, aperture, and shutter speed for both exposures. Also, answering your question in a comment on Rafael's answer, "The thing that bothers me is that the exposure meter on the analog camera was showing that the image is too bright and the exposure meter on the digital camera was about perfect exposure." There are two fundamental problems with this:

• You assume both cameras meter the same way
• You assume the film and sensor (and all of its related hardware, firmware, etc) record the same way.

With both of those points I bet you can see where I'm going: you can't assume they are the same. In fact, my experience is that they are definitely not the same -- even though I have not shot either of the cameras you have, nor the Ilford film, and infrequently Portra 160.

Various films and digital both have ISO values assigned to them but those are really just rough values. In the days of film you would have to go on your experience to know if the manufacturer suggested value was accurate or if you wanted to choose something else; example: many shot Fuji Velvia 50 at ISO 40 to capture more shadow detail. This is something that is measured in modern DSLRs: DxOMark shows that the 5DIII is actually underexposing from nominal ISO values.

Film and sensor results also vary because they target different results. You know that from simply shooting color and black and white film and seeing that they look different, but other films also have their own unique look (try also comparing to Velvia and Kodachrome). None of those options directly align with what the 5DIII create for color. DSLR options also vary with raw and jpg options, as well as their color space setting, and other in-camera settings such as contrast, saturation, and of course auto-anything makes it difficult to get consistent results.

So, to start with, no, you will not get the same results from both mediums. Digital better affords us the ability to match film -- again requiring experience and tools like VSCO film packs to help get the desired results.

Your film was overexposed. The B&W at 400 ISO, f/1.8 and 1/1000s you would have an exposure value around 9.6. The color at 200 ISO, f/1.8 and 1/1000s would give you an EV of 10.7. The 1 stop more dynamic range on the digital allowed for slightly better compensation in the processing. Had you done a 1 stop pull on the film your results may have been closer. (You could also push your digital image one exsposure and get similar results.)

Daylight would be between 12 and 16 EV.

EV for Camera Settings

A = f stop 
I = ASA/ISO
s = Shutter speed in seconds

EV for Lighting

L = Illuminance in Lux

Sorry if I missed this and someone has already pointed it out, but here goes.

In an attempt to make your camera seem better than it is (or other reasons I don't know), manufacturers often don't accurately set the ISO. When your 5d mk3 says it's at 100 ISO, it's actually at about 80, you can see the measurements here: http://www.dxomark.com/Cameras/Canon/EOS-5D-Mark-III---Measurements

This makes the camera look like it has slightly better noise values (or how do you call this?), because at 80 ISO it obviously performs a bit better.

This also explains the slightly darker exposure of your digitally taken photo, because 100 ISO film should be the same as an 100 ISO sensor, but your sensor is not actually at 100 ISO.

I don't know if film manufacturers also trick arround a bit, but I don't think they do because they can't compensate exposure and aperture to compensate the slighty off values.

In normal shoot (not long exposure) digital and film should have exactly the same result if it was exposed exactly at the same time (ISO means international organization of standards). Now, the question is, is your film camera still have an accurate shutter exposure? This is the issue of most old film camera, since it's mechanical and shutter sometimes becomes sticky (slow)