Repeating, the newer lenses are sharper, but remember the 5d3 came out before the 24-70 2.8 ii (so pros used it), and even pros stay with the 70-200 1, because it's so great, that's why they still produce the non-is.
People need to remember that these were the greatest lenses at one point, kind of like the canon fd L lenses, and the 6d (5d2)
I know 2.8 is awesome, but selling your 24-70 could let you get the 24-70 f4 is or 24-105, just for the sharpness/versatility, iOS will save you from f4.
The 70-200 isn't worth selling, you wouldn't get anything better besides the mark ii.
Or you could wait and see what the new tamron does.
But in conclusion, you won't suffer from the older lenses on the 5d3, even all the older ef lenses are designed to work, they don't say all lenses work with all camera produced since 198X