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If you were going to spend the money, which would you buy and why?
EF 70-200mm f/2.8L IS USM or the EF 100-400mm f4.5-5.6 L IS USM
I bought the 70-200 and a 1.4 extender. (aka how to make a really good lens into a pretty good lens)

Some days I wish I had the 100-400 instead. Other days, the 70-200 and the speed are just perfect. With the extender it's just fine.
Next on my list is the 300mm L f/4 prime. A real bargain lens and it takes me past the 200. I can throw the 1.4X on it and have 420. Hey look, everything from 70-420 covered now.
Don't be fooled by the
field of view change, the 200 is still just a 200! It doesn't magically become a longer lens because you put it on a smaller sensor. You are just getting 62% of the full image, which makes it appear like the view you would get from a 320. You don't get more magnification.
You Don't Get More Zoom!
One lens test with the 300mm f/2.8 vs the 300mm f/4 showed that for film, there was a measurable difference in sharpness. For digital it would mean you needed to be shooting at 11mp or more to see that same difference. At 6-10mp you might find no noticeable difference.
Putting an extender on the lenses above slows down the autofocus. Which means the 100-400 by itself will focus faster than the 70-200 with an extender.
I bet I spent a month deciding between the two. Now that I did, I can answer your question. No matter which one you get, you will be happy!
If you want the lens speed, take the 2.8, if you want longer range, take the 100-400. What most of would like is the imaginary 100-400 L IS USM 2.8-3.5, for the same price... right? :lmao: