I use both 7D and 5DII (and still have 50D backup cameras). Haven't used 6D yet, so don't have any personal experience with it and can only parrot what other people think about it.
7D is a far better action/sports camera. It's AF is much faster and more responsive, better able to track moving subjects in AI Servo. You will have more "keeper" sports shots with it than with the 5DII. Just based upon early reviews, I'd expect the 6D to be a little better than 5DII, but not up to 7D AF sports/action standards.
Personally I don't worry too much about frame rate differences, because I try not to "spray and pray" any more than necessary, though I do occasionally use bursts of shots at a higher frame rate in certain circumstances.
7D has 19 AF points, all of which are dual cross type. It also has a discrete chip driving AF, much like the 1D series cameras (along with dual image processors to support higher frame rate shooting).
The 5DII pushes everything through a single processor, and it's image files are larger than 7Ds. It has 9 AF points visible in the viewfinder, with only the center one the "better" dual axis type. 5DII (like 5D classic) also has 6 hidden Assist Points that can be optionally enabled, clustered right around the middle one. It's sort of like "Expansion Points" but only applies to the center point, only two of the Assist Points are the dual axis type, and they only work in AI Servo mode.
Depth of field actually isn't any different, one size sensor to the next. If you use the same aperture and focal length, standing the same distance from your subject, DOF will be exactly the same. What is different, with a full frame camera in order to frame a subject the same way you did with a crop camera, you will either need to move closer or use a longer focal length, either of which will cause shallower depth of field.
Part of the partial myth about shallower DOF is probably due to differences in the viewfinders. The somewhat larger finder of a full frame camera more clearly displays DOF. The smaller finders of crop cameras often don't show DOF as well, you can end up with shallower DOF in your images than you expected, based upon what you were seeing through the finder when you took the shot. The 7D actually has one of the largest and best viewfinders of any crop camera, so is a little better than most. Due to use of an active matrix/transmissive LCD focus screen, the 7D's viewfinder might not be quite as bright, too.
When it comes to high ISO and noise handling, I feel 5DII is usable about one stop ISO higher than the 7D. I also feel the 5DII's AF system is capable of achieving focus in slightly lower light than the 7D (although Canon rates both of them the same, to -0.5 EV).
I do not have 6D, so can't really compare directly. High ISO still shots it appears RAW are roughly the same as 5DII, or maybe less than a stop better. But it appears be able to shoot one or two stops higher when doing in-camera JPEGs. In other words, improved high ISO performance is done through software, not hardware. Canon rates the 6D's AF system to -2EV, same as 5DIII and one and half stops lower than the 7D or 5DII. However, check user reviews to see if this is accurate or not. Without any personal hands-on experience, I can't really say. Reviewers seem to rate the overall 11 point AF system of the 6D a little better than the 5DII, but not as good as 7D or 5III. Of the 11 points in the 6D, only the center point is dual axis. And, like 5D/5DII, it pushes everything through a single processor, though it is the latest and greatest Digic 5 that's supposed to be a significant upgrade over the Digic 4s in 5D/5DII/7D.
i don't shoot video with any of my DSLRs, so really can't comment on that.