Jacob,
I think that buying both is a good idea. My frame of reference comes from the fact that I sold my 70-200 when I bought the 100-400 and I regret it. The 100-400 is very large and heavy. When I'm backpacking or hiking I really wish that I still had the 70-200. As it is now, in those circumstances, I generally leave the 100-400 home because it's just too big.
I think that buying both is a good idea. My frame of reference comes from the fact that I sold my 70-200 when I bought the 100-400 and I regret it. The 100-400 is very large and heavy. When I'm backpacking or hiking I really wish that I still had the 70-200. As it is now, in those circumstances, I generally leave the 100-400 home because it's just too big.