Here is what I did on the issue, I had the same debate but the 600mm wasn't really high on the list for me but I did look into it.
1. I really wanted the zoom feature of the 200-400mm, for sports this is great unless its like a night time game, then the extra stop of light might be a bit more usefull but make me move around much more and possibly miss a shot. Since I pretty much figured that if I was shooting day time sports with a zoom I figured the 70-200mm VRII with a 1.7 TC-E could suffice unless I got a lot of request for this type shot. This gives me a 120-340mm F4.8 for my daytime stuff.
2. Now the choice between the 400mm and the 600mm, well the 400mm is a bit more versitale when I picked up my lens since the smallest F stop cameras could autofocus was F5.6. If I used a 2.0 TC-E I could get the same reach as the 600mm with a TC-E 1.4 but would problaby have to sacrifice some quality for my combination. The price was another factor, the 400mm was a tad cheaper and the finishing blow to the 600mm; I can pack my 400mm 2.8 VR lens in a pelican 1510 case that is rated as an FAA carry on item. I will say that some smaller planes you have to use the check bag at the ramp but most larger planes it fits in the overhead bin just fine.
This was my thoughts on the issue but depending on if your getting paid for this or its more of a hobby would make me look more into the issue of what I really need out of my gear.