A 5D III and 7D II are really in different categories. Both are high-end cameras.
The 7D II is optimized for action photography... it has a blazingly fast shutter burst speed.
The 5D III has a larger full-frame sensor and the sensor is more sensitive to low light with less noise at high ISO.
The 5D II had a primitive focus system but the 5D III got the same focus system that the 1D X has (with one minor nuance). The 7D II basically got the same focus system, but it's been slightly improved. Also because the 7D II has a smaller sensor (APS-C) the "coverage area" of the AF points appear more spread across the sensor (on the 5D III they don't reach as far into the edges of the sensor.)
For this reason, the 5D III's focus system is actually extremely good (among the best in the industry) for action photography, but it cannot compete with the rapid burst speed of the 7D II for action photography.
If you're doing "action" (sports, wildlife in motion, etc.) then you probably want a 7D II.
If you're doing mostly non-action photography (landscape, nature, portraiture, and especially anything involving low light) then you probably want a 5D III.
So it's hard to say one is "better" than the other... since they are optimized toward slightly different usage.
But one last difference on the lens topic...
Canon EOS cameras that use APS-C size sensors (like the 7D II) can use ANY Canon EOS lens (past, present, and presumably future) with the exception of the special "EOS M" lenses that are designed for use exclusively with the "Mirrorless" EOS bodies (the EOS "M" series bodies). That means you can use any EF, EF-S, or the specialty lenses like the MP-E, or TS-E lenses as well as any 3rd party lens designed for Canon EOS cameras.
Canon EOS cameras with larger sensors (full-frame like the 5D III and there were some cameras with APS-H sensors but they don't make APS-H sensor cameras anymore) cannot use the "EF-S" lenses. They can use any EF, MP-E, or TS-E lens... just not the EF-S lenses.
The EF-S lenses take advantage of the fact that since the sensor is smaller, then the image circle projected into the lens can also be smaller and this can be used to reduce the size of the entire lens (and it saves money). But these lenses are specifically designed for use with cameras that have APS-C size sensors (like the 7D II).