The 5DIII beats the 5DII in everything. I agree with some of the points made above, that AF speed, flexibility and accuracy, combined with a much improved low light performance are the key differentiators. I still have a 7D, which I have kept for those cases when distance is a real issue, but I rarely use it now. Because of the improved AF and the excellent resolution, you can crop the 5DIII images and get excellent results. With the 5DII I limited those crops to images with still or slow moving objects.
I have some issues with AWB though, which makes shooting in JPEG a no-go for me (easily fixed in Lightroom from RAW, so not much of a problem really).
For various reasons I also upgraded my 1DMkIV to a 1DX, but 6 frames/sec. on the 5DIII is (almost) sufficient for most of my action photography (soccer and birds in flight), so I am actually not sure if that upgrade was necessary, even though both AF speed and accuracy and low light performance are a couple of notches better on the 1DX.
A nice feature on the 5DIII is the silent mode. For weddings and other events, including wildlife, where you want to be as quite as possible, that feature has real value.
For me the upgrade to the 5DIII is a no-brainer.