7d has a separate processor JUST FOR AF... the 5d3 doesn't.
The 5D Mark III has a dedicated processor for the AF:
From the Canon site (and many many other sites)
Both the 1D X and the 5D Mark III use dedicated AF microprocessors; these AF microprocessors are not DIGIC chips. The increased sensitivity of the focus system has also allowed for faster predictive focus measurements. Increased processing power is another factor to the 5D III's excellent AF performance - "The dedicated AF processor is four times faster than the one found in the EOS-1D Mark IV.
Also my 5D mark III is very close to 6 FPS.
Not sure why his 5D mark III is slow !! , make sure noise reduction is also off and battery fully charged.
Noisy images at 100 ISO !!!! , please post sample images so that we can see what is wrong.
If your 7D output is less noisy then for sure something is wrong.