As a very happy 7D user, and assuming all other factors are equal... go for the 5D3.
More recent tech, better high ISO, better & more GOP options (DSLR video is either very compressed or very very very compressed, the 5D3 at least lets you choose the least bad option) and the option of RAW video output if you are really very serious. There is far less moire / aliasing on the 5D3 (do not believe anybody who tells you there is none) and there is a headphone socket for audio monitoring.
I'm going down the C100 route as video is more important to me that stills. And my 7D exceeds my ability and aspirations as a hobby stills photographer. If you are very serious about video you may want to look beyond a DSLR form.. The great thing about the c100 is that it is a more natural fit for my lenses.
There are somethings to be said for the 7D however:
Great at low isos and medium isos if you use 320, 640 etc.
Cheaper lenses, particularly at the UWA end.
Here's a big thing, depth of field. The object seems to be to get as little depth of field as possible, to emulate the so called film look...
Beaten to death. The film look also requires proper lighting, art direction (colour and light pull your attention, you want a closed set up, where you are in control of anything that is exposed, not at the mercy of mixed lighting etc) and as 135 / leica / minature format DSLRs have sensors that are larger than s35 movie film the effect is potentially more pronounced than you would ever see in a feature film.
I admire the flexibility that say an f1.2 50mm and 135 / leica / minature format DSLR gives you, but I can't imagine ever actually shooting at f1.2, unless the subject was a fair distance away and I really needed the low light capability.
I find that I get more managable depth of field with APS-c / s35 format sensors. You still get that great bokeh with the right lenses, you still get the great smooth fall off wide open, just your depth of field is significantly increased around the focus plane, a huge help when working close, you get most of the desired aesthetic, and less of the pain in the ass requirements for hyper critical focusing, the 7D and it's ilk are that bit more forgiving.
For example in an interview situation I would maybe use a 70-200 f2.8 (my version isn't parfocal, but thats a different issue) and I know that once my camera is set and the subject set that I'll usually have enough focus latitude to permit slight movements by the subject, as folk naturally do when talking.
On a 135 / leica / minature format DSLR you are going to have far less latitude, which may be tolerable on your rear monitor or 7" marshall, but will look awful on a 50" plasma or projected.
It is something to bear in mind.
The 5D3 is the better of the two cameras you mention, but for video, the 7D may be fractionally easier to work with in my experience, and if you are buying exclusively for video I would actually recommend something else altogether.
The form factor of DSLRs is terrible, with menus, controls on the wrong side, lens filtering etc, poor audio options. etc etc.