Basically, yes, they're just different. Film and digital both can capture "everything" the lens gives it a lot of the time, but not all of time, and certainly not under strict testing conditions. Very large prints will look quite different, with people often preferring the way film looks when over-enlarged.
In more detail:
Current sensor resolutions in DSLRs are such that you are.. often?.. not really limited by the sensor. In general unsharpness introduced by camera shake, lens properties, and so on will be a larger factor in image quality than the sensor resolution. If you use quite good lenses, good technique, and set things up to fairly close to the best possible settings you can wind up putting an image ON to the sensor that has interestingly more information in it than the sensor can capture. In normal use, usually/frequently/sometimes this will NOT be the case, though.
Modern film is also pretty darn good, probably about the same area. The films that could reliably outperform then lenses they were stuck behind are either discontinued or hard to get, but most of the films we have today will outperform the rest of the camera "much of the time" and under certain circumstances, well, they won't.
So at that level it doesn't really matter. Film, digital, the image being put ONTO it isn't all that great to start with when you go way way way in to the pixels or grains. The results will look a bit different, but the math says that your final results will have about the same information in them. Generally speaking, in ordinary usage, film or digital will give you "about the same" sizes of enlargements before the wheels fall off and it starts to look over-enlarged.
The look of film, especially at higher enlargements, is quite different. Film and digital will fail quite differently when you enter the land of over-enlargement. Without some special handling, digital will simply look increasingly unsharp, whereas film will start to reveal film grain and start to look "chunky" in a particular way that depends, to a degree, on what kind of film you used. You'll have an impression of sharpness from film due to the sharp rendering of the film grain -- the image itself will be soft, but the grains are spiky and sharp.
This may or may not be pleasing and desireable.
Also, you can of course add a grain effect to a digital file and cause it to "fail" in roughly comparable ways when overenlarged.