Both great lenses.My choice would be 70-200 and a 2x converter for some extra reach. If you need 400 mm and the budget is a bit tight; go for the 100-400.
I have the 100-400 which is great, but it uses a funny “push-pull” zoom system which is kinda weird. You do get used to it but it could be an impediment in situations where you need to zoom in and out very often or very quickly. Try it before you buy if you can.
The EF 70-200mm f/2.8 L IS for sure. Why? For no other reason than it’s got a fixed f/2.8 maximum aperture! At the end of the day, your decision depends as much on what you plan to use it for as anything else. It might be worth heading on over to the review section at FredMiranda to see what users are saying about these lenses.
What do you want to use them for?
I too had a similar choice along with the 300mm f/4.
In the end I went for the 70-200L 2.8 IS as I wanted it for sports and needed a fast speed and I already own the 1.4 extender.
This is a great site for reviews/