I know that the T2i (550d) and T3i (600d) both use the same OEM BG-E8 grip. There are some aftermarket grips (that are significantly less expensive than the OEM one) that are specifically marketed toward the T2i. Am I correct in assuming they will also work with the T3i?
You shouldn't have any problems with a grip designed for the T2i working on a T3i. They have the same body shape on the bottom, and both use the same battery. As you said, the Canon grip is identical - the BG-E8, so there is no reason why other brands wouldn't work the same. The only reason one of them wouldn't work for some reason is if it had extra hardware that somehow interferes with the flip out screen(new feature to the T3i.), but I can't imagine that ever occurring. I did find at least one example of an off brand unit that claims to work on both units - B&H - Vello BG-C5.