Comment by cubefox
Yeah, though they are somewhat similar. We could perhaps say the volume of the unit ball is (in some sense) "larger" than the area of the unit disk, because both are measured relative to a radius of 1. So the area of the disk is fewer "units" than the volume of the ball.
Anyway, it seems independently interesting that this value peaks for the 5-ball, or the ~5.2569-ball. The non-fractional difference between fractional dimension of peak hyper volume and peak hyper surface area seems also interesting. (I assume there is some trivial explanation for this though.)
No it doesn't work that way because the units of hyper-volume and length are different.
However, once you take appropriate roots of hypervolume to get same units you can safely compare. Or the otherway round take appropriate powers of length to get same units as hypervolume.