100-400 vs. 70-200 2.8 plus 2x

I love my 100-400 but am considering shooting sports someday. I understand that the 70-200 2.8 is the industry favorite for sports shooting. However, I need the 400mm for my avian photography. Would the 70-200 2.8 with a 2X converter be just as sharp as the 100-400? There isn't a ton of difference in cost.

No it won't

Nope!!!
I just spent the weekend shooting Soccer with the 100-400 and 100-400 and a 1.4. The 70-200 is too short for most of the shooting on a full size field. I don't think you will be happy with a 2X on the lens either. The 100-400 is a great sports lens if you have the light.
What kind of sports are you going to be shooting?

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I have both lenses and the TC. The 100-400 is better than the 70-200 2.8 IS with the TC. But if I had to only get one or the other, I'd get the 70-200 2.8 IS The 100-400 is not nearly as fast or as sharp.

I was considering the 70-200 for basketball and volleyball. The way it sounds, I'd better hang onto my 100-400 and wait until I have the ching for the other, or opt for the 70-200 f4 and hope for the best.

As far as the 100-400 not being as sharp, I'm extremely happy with the sharpness of mine. This was shot with the 50D.

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I considered the same options before I bought the 100-400. I really cared most about performance at 400mm and this comparison shows the 100-400 as a better choice at 400mm:

http://luminous-landscape.com/reviews/​lenses/400v400.shtml

I've been very happy the 100-400. I was concerned with the push/pull design but I have found it wasn't a problem. In fact, it's very nice for use 100mm to get the subject framed (e.g., a bird in flight) and then zoom to 400mm to track them and take the photograph.

Not sure the 70-200 would be fast enough for Basketball and Volleyball. I would think you need 1.8 or so. The 70-200 will be to long for basketball if your on the floor.
Good Luck
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