Originally Posted by sirhc_1
It will indeed be slightly sharper, as well as the other advantages you mentioned. It also has excellent bokeh, even better than the 70-200 f/2.8 IS. If you are willing to give up the flexibility of the zoom, I say go for it. Personally, I've decided that a zoom in that range fits me better, but there's certain flexibility in f/2 itself.
If you're not sure, it may be a good idea to go for one of your other ideas instead, such as a wide angle lens. I don't recommend the 14 or 15mm primes at all -- they are way too expensive to use on a crop camera. I suggest the Sigma 8mm fisheye over the Canon 15mm fisheye, much better value. There are lots of excellent zoom choices, though, like the 11-16 f/2.8 or Canon 10-22. The EF-S 60mm is also excellent.