@vysuon: Both cameras have the potential for great image quality, but have different strengths.
NEX-5n: If you want something that weighs less, and you plan on using it to "point-and-shoot" for mostly still subjects.
EOS 600D: If you want more control over your photography and better capabilities for action photography.
@vysuon: You would really appreciate the lesser weight of the NEX-5n, but in the long run, the T3i is the better performer. If you're looking for photography T3i. If you're concerned about portability, you might want to stick with the NEX-5n
@vysuon: check out magic lantern firmware. you can get yourself a whole host of new features for your T3i with it.
@vysuon: Nice. You'll want to get a couple of extra batteries. Don't buy them at the retail prices though; you should be able to get official batteries on eBay or Amazon for under $15, and knock-offs for around $8 (compared to the retail store prices of anywhere from $60 to $90 each).
@CROM: absolutely correct. you can never go wrong with extra batteries.
@vysuon: which lens did your gf get with the 5n? the 18-55 zoom or 16 prime?