The answer for you and the situation you have outlined hinges on the answer to the question, "How good is good enough?" The corollary to that question is, "How much more are you able and willing to spend to get just a little bit better?" And perhaps most importantly, "Do you have or are you willing to obtain the knowledge and skill to take advantage of those increased capabilities which often require a higher skill level to operate?" It's no different than being able to drive a Toyota Camry with an automatic transmission and considering a Ferrari Testarossa with a non-synchronized manual transmission: can you double clutch and synchro-shift? Can you handle a high performance rear-engined vehicle with a very stiff and unforgiving suspension in a fast curve?
The biggest difference between the 6D and 5D Mark III isn't image quality, it is the autofocus system. The 5D Mark III has one of the best AF systems in the world that stands head and shoulders above the AF system of the 6D. Not only in terms of the number of focus points and the configurability of the system, but also in terms if accuracy and shot-to-shot consistency. If you are shooting any kind of action, sports, or other subjects that are constantly moving the 5D3's AF system will give you a higher keeper rate and allow you to catch images you probably couldn't capture with the 6D. But just like any piece of high performance machinery, it takes a higher level of knowledge and skill to coax the most out of it.
The PDAF (viewfinder based) system of the 70D is somewhere in between. It is highly configurable with plenty of options (more than the 6D, fewer than the 5D3), but as an APS-C camera it does suffer from the narrower baseline provided by the smaller mirror and AF sensor. It also has a fairly steep learning curve, but not quite as steep as that of the 5D3.
In terms of Live View AF, the 70D does afford continuous AF while shooting video. With STM lenses it works fairly well, but the downside of most STM lenses is that the optics are not usually premium grade. And no matter how good the CDAF is, a seasoned pro can outperform it because she knows before the shot begins where she wants the focus to move during the scene. Most pros still tend to shoot using manual focus with better lenses when doing video with a DSLR. Often they use add-on focusing rigs that engage the lens' focus ring to provide smoother control.
In terms of still image quality the full frame 5D Mark III and 6D will both outperform the APS-C 70D, particularly when shooting in high ISO/low light settings and when very shallow depth of field is desired.
With choosing between a 5D Mark III or both a 6D and a 70D the question also should be raised as to how often you will need or want to shoot with two bodies. One FF and one APS-C body often works well in a two body setup. You can use a wide angle lens on the FF body and a longer focal length on the crop body and that allows you to expand the range of your angles of view beyond what both lenses could do on a single body.
Finally, one thing you haven't mentioned that should perhaps be your starting point is what lenses do you currently own or are considering for use with your new camera? That's where the real and most difficult decisions are to be made, and where you are really forced to ask, "How good is good enough?" How you answer that question might go a long way towards informing your decision about what body is the best fit for you.