Ever since I got the 15-85 it practically "lives" on my 7D, the 24-105 hasn't seen much use. Here's a test I did awhile back. The first and third photos below are from the 15-85, the second and fourth are from the 24-105. I didn't bring a tripod and let the IS of these lenses did the work.
Both of them look pretty sharp, and contrasts are similiar. Blown up, I think I would give a slight edge to the 15-85 on corner and edge sharpness.
I'm keeping the 24-105 because of its better weather sealing, which may be useful if I have to go out and shoot in harsh winter.









