Hmmm 15-85mm? It costs around 800$(750euro) Wouldn't there be an L lens in that price range? *Not planning to buy one soon, just curious.*
The 17-55mm f/2.8 IS is even more expensive. IMO, the 17-55mm is the best general purpose zoom for APS-C, and the 15-85mm is a close second. Both lenses are of L-series optical quality (as is the 10-22mm), but not build quality. Compared to the 24-105L or 17-40L, those three EF-S lenses (17-55, 15-85, 10-22) actually deliver better IQ than the 24-105 and 17-40 L lenses on the same APS-C camera (and the 17-55 outperforms the 16-35L II on APS-C, I know from personal experience).
The 17-40mm is sort of 'general purpose' (a little short on the long end) on APS-C, the 24-105 isn't in that category (it gives the FF-equivalent AoV of 38-168mm on APS-C, meaning it's normal to tele, and a general purpose zoom should cover wide to short tele).
The only times I'd recommend one of the L lenses over the 17-55 or 15-85 are if you have a 7D (decent weather sealing) and need a sealed lens to use in inclement weather, or if you have both FF and APS-C or are getting a FF in the very near future (weeks/months, not years).