The 6D is 14 bit (as are some other DSLRs), 20 meg with 6.55 micron pixels, 43.04 mm on diagonal sensor. There is also more in camera (DIGIC) processing for noise reduction, color balance etc. So not really comparable to the ASI1600. It might be more comparable to the older smaller sensor EOS cameras.
In my honest opinion, having used a 5D III (which is fairly close to the 6D in terms of performance...the 6D has slightly less dark current noise, both still have banding) quite extensively under good, dark skies...I still think it would be no context between the ASI1600 and the 6D. Because of the extremely low noise and high sensitivity of the ASI1600, the tiny pixels, and the option to either use an L filter with LRGB, or narrow band filters (or both!), you could mosaic a field large enough to fill the 6D frame, and have at least a similar SNR (however, on a normalized basis, SNR would likely be much better), in about the same amount of time it would take you to get a decent SNR with the 6D.
I've been working on a mosaic of the Cygnus North America and Pelican nebula region for a few nights now. I am getting no more than about 37.5 minutes per PANEL, and you can stack four panels to get about a 33.5x25mm FoV. So in 2h30m, you could have a full frame FoV with quality like this:
Here is a 100% crop for examination of the noise details...and, check out the TINY stars...with a low pass filter and the need to demosaic, a DSLR could never produce stars that small...even with smaller pixels. The filter and the demosaicing blur too much:
Also compare the quality of the noise. Even at ISO 1600, which tends to deliver the best noise quality on the 5D III...it is not even remotely close to the kind of clean, low, random noise characteristic you can get with the ASI1600. Even in the poor signal areas of the dark dust...the noise still maintains an exceptional gaussian quality. I'd love to see a 6D produce detail and quality like this at full size in just two and a half hours. An ASI1600 mosaic would also be 64 megapixels, rather than 20...downsample the ASI1600 mosaic to the same pixel dimensions as the 6D image, and you reduce noise and improve SNR even more.
There is no contest here. These are 90 second 3nm narrow band Ha subs, only 37.5 minutes of integration. Possibly outside of a cold fingered mono-modded full frame DSLR (and even then, I'm skeptical, due to the loss of microlenses in the mono-modding process), DSLRs don't stand a chance here.