Sorry, but NO! According to the System Map on pages 354 & 355 of the 6D's instruction manual, the Remote Controller RC-6 (available for about $25 from Canon and other camera outlets like amazon, B&H, etc.) works on the 6D.. see http://gdlp01.c-wss.com/gds/8/0300009238/01/eos6d-im-en.pdf and go to p355 to see other more advanced controllers also compatible with the 6D. I might add that the RC-6 is also compatible with the EOS 5D Mk II. I hope I was helpful! I think the 6D is a very nice camera and I hope you're enjoying it too.
Anytime you can get a Canon L-Series lens, you are probably going to do pretty well. I noticed a lot of the "answers" didn't really address your question, just stated they already HAD lenses. I had NON-L series lenses before buying this camera, and when I had the chance to get the camera with an L-series lens, I definitely went for it. I have not been disappointed. The only lenses I have used that have ever been sharper than this one are the L-series Prime lenses. Otherwise, the kit lens is quick, sharp, has a nice bokeh to the pictures at the low F-stops, all in all, a nice lens.
Some are and some aren't. The 7D can use EF-S lenses (they are lenses with a white square at the connection point) and EF lenses. The 6D can only use EF lenses (they have the red dot at the connection point). EF-S lenses cannot be used with a 6D
It depends on what is more important to you and how you shoot? The 7D has lots more AF points. Would you be using them? Do you currently rely on a crop sensor to get that extra focal length in your EF lenses? How used were you to shooting 35mm?
Personally I can see the merits of having both. I love my 6D and full frame, but there are times absolute real estate of the sensor size isn't necessary and I'm looking to replace my aging, but solid, 40D. The 7d has a larger buffer, more processing power by 100%, dual slots, but a smaller sensor size for MP size. Are you shooting more video than stills? The 1st 7D excelled at that.
I personally will always steer towards sensor size. I have images from a 11MP 1Ds that beat 15MP crop sensor cameras (not to mention 1 2/3" sensor 15MP cameras) simply because the MP weren't constrained to a small sensor size.
I realize this really doesn't help answer your question and only asks more. But the camera is a tool, and it's very rare that a camera comes along that is that swiss army of cameras that does everything better than all the rest. Good luck in your decision.
The cds include the Standard EOS digital software that comes with each new Canon dslr, a detailed instruction manual, Canon Digital Photo Professional for processing RAW images and instructions for RAW processing.