24-105 is not wide enough for APS-C.
Eh, depends on what you'll be shooting though. I found it was good enough outdoors...only if you do wide landscape shots will it seem inadequate. Indoors, it's a different story though- 24mm will not be wide enough for group shots in small to medium size rooms.
So...my thoughts- I'd say for general walkaround use, the 24-105 would be my choice. For indoor event photography I'd go for the 17-55 (which is what I used to have)...if you want to do both, and never plan to get an FF camera, 15-85 is a good compromise.
Personally, I didn't care for the 15-85 because of the variable aperture and lack of weather sealing for extensive outdoor use.