I have owned both 70-200 f4 L IS and the 70-200 f2.8 L IS and found the f2.8 had a little too much volume to walk around with.(so i tended not to use it as much as I wanted to.)
The f4 IS on the other hand is light and has very nice picture quality (so I tend to take it everywhere).
A lens that is not used is a dust collector in my eyes and must go to a better home.
Sold the f2.8 kept the f4
You own nice prime lenses for when you need a faster shutter speed in low light.
So I would go with the 70-200 f4 L IS.
Just my opinion
