Despite its age, the 100-400 is a far better option. With the 2x extender on the 70-200 f/4 you'll lose AF with all but 1 series bodies. And at a max aperture of f/8, you'll struggle to stop action. And the IQ at 400mm with the extender will be worse than the 100-400 at 400mm (not to mention a stop slower).