The T3i is a little better than the T3 in a number of areas -- higher resolution, shoots full HD video, bigger LCD screen.
Better pictures? Not much of a megapixel whore here -- better pictures have more to do with the photographer than the camera most times (fine cookware rarely creates a chef). They're all pretty good these days.
Just ran across an interesting site that lets you compare.
Here's the T3i against the Nikon D5100:
http://snapsort.com/compare/Canon-T3i-vs-Nikon-D5100 (Nikon wins that race). The D5100 is being discontinued for the D5200, so there are deals to be had.
In the Nikon/Canon/Fuji/Pentax, etc. wars, I'm an advocate of trying 'em and going with what works best for you. I find Canon DSLR's to be awkward to use, but other folks say the same thing about Nikon. Couple weeks with either and it's no big deal. You really can almost shop for deals at this level -- they're all good.