Any one who owns a NEX-5N will pretty much knows what kind of image quality can be expected from the NEX-6. The image sensor on the NEX-6 is based on the one from NEX-5N, with the exception of on-sensor phase detect pixels. In theory, these phase detect pixels should count as dead pixels since they don't produce picture elements and have to be mapped out in firmware when picture is created, just like mapping out dead pixels.
I was very happy with the image quality of the NEX-5N. Superb dynamic range and very good high ISO quality. The only thing I didn't like much, was the jpeg from the camera. It just wasn't anywhere as good as what can be obtained from RAW conversion. The NEX-6, however, has a very good jpeg engine. If you shoot only jpeg, you will be very pleased. The colour fidelity is improved and noise/compression artifacts have been mostly eliminated in low ISO. Comparing NEX-6 jpegs to my 5D classic jpegs, I still see some difference, that the Canon is slightly better, but not by much.
Even though the camera can shoot to ISO 25600, I wouldn't bother with anything higher 6400. I would be comfortable with ISO 3200 and use ISO 6400 if I have to, but anything over that, is basically for marketing claims. Sure you can make pictures with it, especially with black & white, but the noise level would be too much, and details too little.
I can't claim the NEX-6 has the best image quality of all mirrorless cameras, because I haven't used the others, but it's better than any Canon Rebel/60D/7D can produce. It's good enough for me.
Elevator on Skylon Tower - NEX-6 & Minolta RF Rokkor-X 250mm f5.6, ISO 800.