My 2 cents. (I'm not familiar with the 3rd party lens, so I'll leave that to others...)
With a 1.6x crop body, your choices would be slightly bit different from those of an FF body. Buying a 24-105mm f/4 would work if you are considering the switch to FF later on, but in the mean time you'll have a "missing link" between ur 8-16 and this one.
Of course, you also have the option buying the L lens at the time you switch to the FF system. Who knows, maybe you'll see a 24-105mm successor couple years down the road by the time you do it.
Since you've already mentioned the 17-55 f/2.8, I'll just add two more from the EF-S lineup that would work as possible choices for walk-about lens: the 18-135mm f/3.5-5.6 and 15-85mm f/3.5-5.6. The good thing is all these models have IS, so you don't have to worry about that.
Affordable - 18-135mm> 15-85mm> 17-55mm
Reach - (you'll have to decide here; 18-135 has the longest range, while 15-85mm is the widest out of the 3)
Speed - 17-55mm >>>> 15-85mm/18-135mm
As for picture quality, you might have to ask people who actually owns the lens, but I think it's safe to assume that 18-135mm will be at a disadvantage when compared to the other 2.
Another note is that 18-135mm lacks USM among the 3. With USM, you'll have less noise and faster focusing time.
PS: If you are really considering to buy a lens that would work now and at the time you move to FF, the choice IMHO would be 17-40 f/4L. The UW lens could work as a standard zoom if push comes to shove (roughly 27- 64mm equivalent for the 60D). But you won't have the IS, so that should be taken into consideration.