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I've tried out a few 200mm lenses on m4/3 and Fuji X, so they should act similarly to how it'd work on the NEX. The best of the 2.8's for a reasonable price I'd say is the Canon nFD 200/2.8.
It has a fair amount of longitudinal CA, and a good bit of purple fringing on high contrast edges, but it is very sharp, even on m4/3's crazy pixel density.
You'll likely need to go up a good bit in cost for some big improvement in the CA department at f/2.8. If you're willing to go to an f/4, I think the Zeiss 80-200 and FD 80-200 f/4L (note the L) should be better corrected in that regard. I know my FD 50-300mm f/4.5L controls CA and fringing MUCH better than the 200/2.8, but that lens is beastly large, rare and usually a little pricey as well (though I got a great deal.
Two shots with my 200/2.8: