From Canon T3i to Nex-6. Am I giving up some image quality?

Maybe not image quality, but you will be giving up some other things, such as effective exposure bracketing in raw, optical viewfinder and reversable screen (the screen of my NEX5n is extremely susceptible to scratches). Maybe also the flash ability. Also, the lens selection of the Canon is much better and maybe also the colour rendition.

I wouldn't do it. Get an NEX5n for travelling light but definitely keep the Canon: if in doubt just look at the amazing shots that people take with the Rebel series.