I would normally recomend the 15-85 in this instance but as you already have a 10-20 you don't need that extra width.
I personaly think 24mm is too wide for a crop sensor walk around lens so if you want to be changing lenses all the time get the 24-105 to go with your 10-20. If you want a single lens you can take out and not have to cary any extra gear, get the 15-85
Some people need lenses with red rings on them to help with photographic confidence
yeah I got that wrong, Not wide enough
