I have to admit I'm perplexed what criterea you're basing your decision on. But then I do confess I struggle to understand, why would anyone be so hung up about remotely contolling a camera with an iphone5!
Surely if I had so little interaction with my camera, I wouldn't bother with a 6D let alone a 5d3!
A Good camera for all that "whack it on facebook immediately" crap would be an iPad4. Its got a built in low light ability 12 mps - instant onto social networking sites, and a brilliant display. (Sorry for being mean just could not resist that jibe)
However If you are actually going to really enjoy photography, and you seem to analyse your purchase process in detail ( ironically actually rather like I do) I can tell you now, you would regret geting the plasticy 6D, with the cramped AF.
I can happily take 400 clicks in a 4 hour shoot. Go and do that a couple of times and then tell me if you would be happy to 1/2 press and recompose! No Way. Just buy the 5D3 and lash out on the Best value for money lens the 70-300L F 4-F 5.6 IS USM and go and take some quality portraits, and a few outside shots sports etc.
G'tee you will be sending me a pm saying "thanks for saving me from a big mistake!"
And my other prediction is you will take a lot more than 2000 pics per year!
Which focus points do you use on your 5d3 for rule of thirds photography?