If the choice is based over which camera allows me to produce better photos, I'd choose the 5D mark III over the 70D hands down and never look back.
I regularly use both a Canon 7D and a Canon 5D mark II. When I am shooting with only one body it is almost always the Full Frame 5DII. To my eyes there is a visible difference between images made with each body, especially in high contrast/high dynamic range environments and in low light environments. The only times the 7D gets the nod over the 5DII is when I have plenty of light that isn't harsh and I need the extra reach of the 1.6x crop factor or when I need the faster handling of the 7D to catch sports/action. I rarely mount any other lens on the 7D than an EF 70-200mm f/2.8 L IS II. It is one of the best mass produced zoom lenses in the world. I use that lens plus a variety of shorter "L" zooms and non-"L" primes on the 5DII, so the difference in image quality has nothing to do with the quality of the lenses.
The focus system of the 5DII is slower than that of the 7D, but both are about the same in terms of accuracy and shot-to-shot consistency: neither is anywhere near exceptional. In my opinion the two biggest weaknesses of the 7D is the inconsistent focus system and the low light performance in terms of noise. For the 5DII it is only the focus system inconsistency.
For the 5DIII vs. the 70D, the image quality comparisons are very similar to those of the two bodies I use: the FF will noticeably outperform the APS-C sensor in terms of dynamic range, low light performance, tonal range, and color sensitivity. Here's a side-by-side look at the sensor performance of the 5DIII vs. the 70D from DxO Mark. To see the specific results of various tests, click 'Measurements' and then each parameter you wish to compare.
In your case, the difference in terms of handling speed between the 5D mark III and the new 70D is much less than that of the 3.9 fps 5DII and the 8 fps 7D. The other key difference in your comparison is the far superior accuracy and consistency of the 5DIII focus system over the 70D focus system which is the same basic system as the one in the 7D. The focus system in the 5DIII is the same one found in the 1D X. Even when only using the center focus point, you will find that shot-to-shot consistency will be much better with the 5DIII when used with the newer lenses that more precisely communicate with the body how far they have moved. But I would also encourage you to learn to harness the capabilities of that very nice focus system.