Having a 60d myself, I can tell you that the HUGE difference you will see will be in ISO performance. I found the AF on the 6d plenty reliable. I even pushed it in crazy low light with my 50 1.8, which doesn't have the greatest AF motor, and it worked. Worked better with my 70-300VC with it's USD motor.
It is pretty much the exact same size and weight of the 60. For all of the gripes people have made over the AF specs, for portrait/normal shooting/walk-around/still subject, I had zero issues. Never tried servo mode or anything fast moving.
Personally, I found the 1/180 flash sync more of a let down as I tried to shoot one person jumping into another's arms. I had to use the 60d for faster sync to freeze the action so HSS is something I would be looking into if I got a 6d for what I do.
Other than that, it delivers and I don't think you'll be disappointed at all...especially when you look at your high ISO shots