I'd go with the 5D Mark III, because you're not going to be photographing much with a camera that doesn't exist.
Well as you might guess there will be a replacement on the 7D so that for i mentioned it as a 7D II, but it can also be a 8D...
Welcome to the forum! If you hadn't gathered from the responses, there is a fair amount of burnout here from people asking about purchasing cameras that don't exist yet. As there hasn't even been a solid CR2 on the 7DII, let alone any actual hands on experience, it is impossible to give recommendations for or against it.
The general rule of thumb around here is if you need/want to take pictures now, buy what you want now. If you are waiting for some specific feature, it might make sense to wait, but if it's just waiting for something better, there will always be something better coming out and so you wait forever.
I can cite my own position on these two cameras, as that is something I'm weighing. I currently have a 7D, and although I am less than thrilled with the IQ, it does what I need it to do for the time being. I've been very tempted by the 5D3, but as I am almost exclusively a sports shooter, I'm waiting to see what the 7D2 brings to the table. I would also like wifi in my next body (which is a strike against the 5D3), but that's not a deal breaker. Should the 7D2 not have the high (and low!) iso quality that I'm looking for, along with wifi, I'll likely get a 5D3. But in the meantime I can afford to wait because I'm not missing any particular photo opportunities with my current setup.
Hope this helps!