One of 3 lenses I've used extensively on both crop and FF (the others being the 24-105 and 70-200 2.8 II). Its relative compactness is a plus, and it has strong performance where it matters most (300mm f/5.6). OTOH, the 70mm end can be a bit weak, particularly on crop.
On FF it's a decent general telephoto lens, mainly for outdoor events. With the hood removed, it offers a decent amount of reach without being too overbearing which makes it work well for candids (people). And the sharpness is on a very high level, so no complaints there. The only issue is the f/5.6 at the long end limits its use to mainly outdoors/daytime shooting, which in turn limits versatility. The IS system is pretty good, so if you're shooting still subjects this can be overcome to an extent...but AF accuracy still takes a hit in the dark.
On a crop sensor...I think this is actually where this lens really shines. Despite weaker performance at 70mm wider than 5.6, it offers tremendous reach ability in a very small, relatively lightweight package. In fact, this is what I currently use for animal photography, although 300 is still too short for most birds (looking at a 400/500 for that, perhaps with TCs).
I was going to sell this lens to trade in for the new 100-400 when it was announced, but since I didn't need the money right away I decided to hang on to it for the time being. Glad I did. I think this is Canon's smallest 'white lens' - not sure why they made it a white one to be honest, I'd have preferred if they left it black. I suppose they had to differentiate from the non-L version, but the 24-105s co-exist both in black...shrug...