Check out SLR Gear reviews on these lenses. Take a look at the Blur Charts that represent IQ.
Surprisingly the f4 lens has slightly better IQ, but with much less weight. Unless you need f2.8... I wouldn't upgrade at all.
I own the 70-200 F4is and the 300mm f2.8is. The only lens I have ever used that even comes close to the 300... is the f4 70-200.
I may have the wrong 2.8. The 70-200 f/2.8L IS II is sharper than the 70-200 f/4L IS. There are other versions of the lenses and I've lost track of which ones we're doing here, but the ones I mentioned, the 2.8 is far superior.