I've got that lens from my days of using a 1000D (Rebel Xs) and I used it to take some amazing moving shots of cheetah hunting in the early morning light at Kruger and a long-distance shot of a leopard in a tree.

On lesser Canon DSLR models the problem might be that there's too much in the shot at different focal distances - I used to rely on having a large field of view and cropping it later - but this gives the processor too much to do and it usually dithers. When I started trying to get the final shot I wanted in the frame of the camera I found it responded better.

I have used the 70-200 f2.8 before and didn't like it much because it was so heavy. It induced more camera shake than the better IS gubbins removed unless you were using a tripod (i.e. more weight).

What body is your lens on?

(PS: I only really have 3 years of DSLR experience).