I'm not too familiar with the 60D (and have used a 600D/T3i only in a store), so I can't speak to the advantages of one over the other. But I do have a T2i, and it's been more than sufficient for every stage of my learning to use both the photo and video features. I started out using auto and manual focus, and thinking I was the king of everything, but have evolved into really understanding the camera. 98% of the photos and videos on my site are shot with a T2i, and you can see the change as I learned - not necessarily terrible pictures in the beginning, but you can see the progression as I learned to use the camera.
I guess what I'm saying is, buy the cheaper camera. Things add up afterwards - lenses, tripods, filters (I just got a polarizing one for the T2i), and anything else you had no idea existed until after you got the camera. :) And for me, at least, I haven't yet found myself wishing I had a better camera (except maybe for more customizable movie settings, but then you start getting into professional film cameras).
-Leadfoot