I have the smaller f/4L IS USM lens on my 7D and it is even sharper handheld than my nifty-fifty (50mm f/1.4) stopped down to the same aperture.
I read a review recently that listed 3 key differences between the f/4L IS and 'non-IS', obviously firstly the Image Stabilization, secondly; the weather-shielding, but also thirdly that it was sharper in the center @ 85mm. If the latter is true, it would be an interesting test vs the f/2.8L Mk II, at that particular focal length.
Last year, whilst shooting some HD video with it I got some really amazing lens flare (as I panned from left to right, you could see the aperture blades shape and some nice colours) + nice bokeh too on some background stuff.
If you intend on using your new 5D3 mainly outdoors, then the f/4 L IS will certainly give you some great images. In terms of image quality, there could not be more than a hair's breadth between these two lenses.
I can empathize with your dilemma, the newer 2.8L is apparently like a series of 'primes' stuffed into a tube, but is definitely big money. Then again the 5D mk III costs a grand more than this lens....so sticker shock should be limited as you should not scrimp when it comes to glass (imagine getting a 1DX and sticking a 50mm f/1.4 instead of a 1.2L on it?!). If I had the cash, I would get the lens before the camera body, but hey, that's just me.