In this case, I think you have to make a judgement call on the longer lens. The Canon EF 100-400mm f/4.5-5.6 will give you better results at 400mm @ f/5.6 than the EF 70-200mm f/2.8 L IS (I) with the 2x Extender at 400mm f/5.6.

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=113&Camera=453&Sample=0&FLI=7&API= 0&LensComp=103&CameraComp=453&SampleComp=0&FLIComp =6&APIComp=2

If you happen to have EF 70-200mm f/2.8 L IS II, then the results are much closer:

http://www.the-digital-picture.com/R...mp=5&APIComp=0

Looking at the ISO chart results should help you decide whether the incremental image quality will be worth the investment. If you're curious, check other comparable focal length lenses (300-400mm) to see how they compare to your 70-200mm + 2x Extender combo.