Having gone back and forth between options, I am thinking a 6D is my most practical choice. ($$$). Of course, I would rather have a 5D Mk III. But that being said, what do you 6D owners find you don't like about the 6D? I really want a full frame and an upgrade to better low light...... Focus points.... well, I guess I can be OK with the few that I would get..... But day to day, in hand, what don't you like about the camera? And what do you like better than your previous camera? Is the joystick too far away for easy point selections? Etc..Currently shooting a 20D and a 40D. Want to put my 17-40 and my 100 to work for me on a full frame body.
I have questions for you, rather than the other way around. Why would you rather have a 5D3? Have you tried one? What type of photography do you do, and how much of it is professional? How much of it is with a flashgun? How often do you shoot above ISO 1000, and how critical is that to you? Do you like grain (luminance noise) in your photographs?
In my opinion, the only reason to have a 5D3, is to make full use of it's autofocus sensor and the extra 2 frames per second over the 6D (which is not all that much difference alone, but the 5D3's autofocus sensor's ability is certainly stellar compared to all other Canon bodies other than of course the 1DX).
So if you mostly shoot on a supertelephoto lens, and you are shooting sporting events professionally and critically...then the 5D3 is an inexpensive alternative to the 1DX, and should be bought instead of the 6D.
If however, you don't really fit into the above criteria, and you are just wanting the 5D3 for the bling factor of having one, then don't waste your money. Put that money toward more and better lenses.
To answer your thread title's question...the only things I don't like about the 6D, are the inferior (perhaps intentially handicapped) video ability due to moire (compared to the 5D3), and the single card slot only using an SDHC card.
That said, I don't think the 6D really needs a CF card slot, unless you are mostly shooting video with it (and especially if ML ever hacks the 6D to enable RAW video capability...which they just might not ever do.)
I do like most everything about the 6D. The grip and ergonomics are better than my 50D (which I promptly sold), and the body is also lighter and every bit as rigid as the 50D. I don't miss the joy stick at all, nor having most of the buttons on the left (on the 50D they were along the bottom). I also prefer the 6D to the feel and ergonomics of all other Canon and Nikon cameras, all of which I have at least played with in a store, if not rented, or tried those of my relative. The 1DX is a fantastic camera, but it is very heavy. If you ever got used to holding it, everything else would feel too small and light like a toy.
There are those who don't like the ergonomics or various other aspects of the 6D. As others have said, that's fine...then don't buy one, or sell it and buy something else.
I feel the 6D is the best overall camera Canon has ever made. The main reason being they were able to deliver world class image quality, and bring it to a price point that is very reasonable....as compared to most of their recent L lenses. Although they seem to be the best lenses in the world, the price reflects that. Certainly those lenses are worth owning, but they are an extreme luxury now.