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

I bought the NEX-7 because of IQ, including DR, and use mostly MF lenses.  I have the kit 18-55 and the 16, and was surprised how good they were, especially the 18-55.  When I want critical work, I use something like my Canon Fdn 35 f2 lens, or a Zeiss Planar 50 1.7, both of which I think will hold up to any glass today.  And with the NEX sensors they will equal or outperform anything short of top-line FF cameras, and even there the difference will not be great.

My point is give MF a try.  It's not the best for everything, but with focus peaking NEX's focus about as well as Leica M's, which offers no option other than MF.  (I don't own a Leica M, but yes I have used one.)  When AF is needed I think you will find the IQ of the kit lens of sufficient IQ that in the real world there is not much difference between it and the Canon glass, especially the non-L Canon glass.

Admittedly if you are doing sports or fast action photography, the DSLR outperforms the NEX's.

Michael