If you don't mind the AF on your rebel, You have nearly the same experience or slightly better with 5D2/6D/60D or pretty much any camera with the 9 Point AF system. You'll have the same issues with it such as off-center focusing with high-speed primes or with moving subjects off-center.
I believe lumping the 60D and 6D AF together is slightly misleading, as the 60D has all cross points. One of my disappointments with the announcement of the 6D was the AF actually being a step DOWN from my 60D's AF. I just couldn't see "upgrading" to something that made quick accurate focus more challenging, despite the wonderful reviews of the sensor.
As to the original poster's question, IMO, the 5DIII makes life with very shallow depth of field apertures quite a bit easier, especially with close up portraiture. Recomposing at f/1.2 - f/2 is hit or miss for me when I want the iris to be perfectly sharp, but having a big choice of accurate AF points makes it work most of the time.
On the other hand, fellow photographers in my area who use 5DII's and Rebels, and who have much better eyes for landscape, street, and found still-life, outshoot me in those categories some of the time, simply because they have a better grasp of composition and natural light--and years more experience.
You have to decide whether the convenience and flexibility of the "better" AF systems are worth the $1k premium you will pay. The "better" choice is the one you can afford and use well. Don't get in a gear measuring match, just shoot, study, process, get critiques, and repeat over and over.