FWIW, I have both for my 5DII &II The 2,8 is very thin dof. The lens is very heavy after a while, it is long and has b big diameter.I find the image as good as my F4L is, lighter, shorter, smaller diameter, and easier to use. May even give some better shots. I yo can afford it I see no reason to get rid of this gem.
I have both the 70-200 2.8 ii is and the 70-200 f4 is, if weight and money aren't an issue go for the 2.8 ii is, it really is an amazing lens, everytime I put it on my 5Diii it just astounds me how good it is, that being said the f4 version is brilliant as well....most times the F4 is attached to my "walkaround"7D, the reduce weight of the f4 makes it easier to throw it around.
I purchased the f4 version first then saved for the f2.8, Sometimes, when I look at my gear, I think do I really need both of these 70-200, the answer is "yes" because I have two bodies....if it was only the 5Diii I would only have the f2.8..
There are some great third party lenses out there, but the 70-200 2.8 l is ii, really is the best " one lens to rule them all"