If you like sporting kind of shots, you would LOVE the 5D III. Many, MANY professional sports shooters use that camera body if they have a backup to their 1D X (that is the top level sports camera at the moment.)
The depth of field afforded to you with the 5D III will make your sporting shots outstanding from what you're used to with the crop sensor.
I think my budget and lack of serious long lenses precludes me getting the 5DIII I looked at the 6D (it's about the same price as the 7D was a few months ago here in the UK But I then run into the lack of ability to Spray and Pray (I like to snap jetskis, kite boarders etc). The 7D works brilliantly for those things, but I find it falls down when I want to take more static snaps in poor indoor lighting. I hate flash (I've never really got the hang of it) and that's why I wanted a 7DII with better noise and hopefully a tad more DR. I might just grab a 150-600mm Tamron and keep the 7D I might need beta blockers to hold it steady with that combo though