The problem is disparate uses. The 100-400 is better for aviation, the 70-200/2.8 is better for portrait, sports and general use. I voted 100-400 because you listed aviation first, and 'pilot' is in your name. The 100-400 is great for airshows. The 70-200/2.8 non-IS doesn't hold up well to the 2x TC (although the IS MkII does). But if by aviation you mean you go to an airshow or two a year, or if you'd prioritize the other uses above aviation, get the 70-200.
Used 100-400s can be had for $1000 - you might go that route, and get an 85/1.8 for portraits and indoor sports...