pros and cons 70-200 f/4 L IS vs 70-300 f/4-f/5.6

Has anyone used both of these lenses? I am trying to decide between the two.

From what I can see on the digital picture the 70-200 f/4 is sharper mid frame and in the corners. Center sharpness is about the same.

Focusing speed? Is there much of a difference?

I like that the 70-200 has a closer minimum focusing distance and is compatible with the 2x extender (even though autofocus won't work @ f/8.0) on my 5d mkii
I also like that it is weather sealed.

On the other hand the 70-300 has a longer focal length and is less conspicous (did I spell that right?) because it is black. It will require less lens interchanges if I want to go from 70mm to 300 mm (no need for teleconverter). It is decently sharp and it is smaller and lighter.

So the question is which one to go with?
Any advice is welcome.