If we were to graph out the "sharpness" or various lenses, my guess is that we'd come up with something like this:

Keep in mind that this is hand-drawn based on my beliefs, not an actual graph of results from tests, or anything like that. Since it is hand-drawn, don't try to read too much into things like whether it might not be more accurate to show more overlap between the two, the spot with a negative slope on the left-hand part of the "Primes" curve, etc.
In any case, let me point to a couple of points this is intended to show.
- On average primes have higher resolution than zooms, but
- There's a lot of overlap between the two
- Resolution of zooms tends to vary a lot more widely
- Conversely, primes tend to be much more consistent
- A lot of zooms have much lower resolution than almost any prime, but...
- the best zooms are better than all but a few of the very best primes
As you reduce the aperture (smaller opening/bigger number), differences between lenses tend to get smaller. By f/8, even poor lenses usually produce decent results. By f/11 they're all starting to get worse, and by f/22 they're virtually all getting pretty poor.