Get the 100-400L. The native 100-400 focal length will be way better than the 70-200 non-IS.
For what you intend to shoot, you won't find a better value for money lens than the 100-400L.
1DX, 5D3, 600D, RX100
16-35L, 24-70L II, 70-200L II, 100-400L II, 50L, 85L II, 135L, 17TSE, 24TSE, 40, 100 macro, 18-55 II, 55-250 II, 1.4x III, 2x III, 600RT x 4
When it comes to gear, it is better to vote with your wallet. Bitching on online forums like a lunatic doesn't get you anywhere!