嗯。

My 70-200 f/2.8 IS (original) is not very sharp (well, it is not bad, more than enough for my purpose, comparable to sample photos on the Internet, so I do not think it is a bad copy) when compared to 500mm f/4 at f/4 or Sigma 120-300 f/2.8 at f/2.8.

So your 70-200 f/2.8 II should be better (my memory was from the original version.  If 70-200 f/4 II comes out, I would expect it to be sharper than 70-200 f/2.8 II at f/2.8.