With wildlife, you often need as long a lens as you can get... so with the 70-200/2.8 Mk II I'd lean toward a 2X teleconverter. 200mm is pretty short for wildlife and 280mm (200mm + 1.4X) isn't a whole lot better. That's especially true if using the lens on a full frame camera. The "free 1.6X teleconverter effect" of crop cameras (7D, 60D, etc.) helps, too.
If considering a 2X, then I'd most likely stick with the Canon 2X Mark III. I don't know that any other brand will work nearly as well on the 70-200 Mark II (I would't even use my 70-200 Mark I with 2X Mark II, there was just too much loss of image quality).
If you go with 1.4X instead, then the Kenko Pro 300 DGX is a strong possibility. By all reports, it's virtually as good as the Canon (Mark II or Mark III, both are pretty good). And a 1.4X leaves your viewfinder brighter, the AF faster and has less negative effect on image quality than a stronger teleconverter. The Kenko DGX might or might not maintain the same level of AF speed as the Canon... I dunno, haven't tried it. The earlier Kenko "DG" is slower than the current "DGX" version... upgrades to AF performance were one of the key features of the new model. For use on a zoom, I wouldn't consider the cheaper Kenko 1.4X MC4 teleconverter. And definitely not the 2X MC4.
The Kenko teleconverters might have one advantage over the Canon... all the Canon Mark II and Mark III have protruding front elements that fit inside the rear of the lens. The Kenko TCs don't. This limits to an extent what lenses the Canon can be fitted to, Canon says the 135/2L is the shortest and the 70-200s are the only zooms, tho there are some work arounds and some make them work on other lenses. The Kenko have less limitation in this respect, but in general a teleconverter works better with a prime lens, than it does with a more optically complex zoom.
According to Canon, the two Mark III Canon TCs are actually designed to slow down AF a bit, for greater accuracy. This is probably offset by faster AF performance in the newer lenses, probably including the 70-200/2.8 Mk II.
From Chuck Westfall: As with previous EF Extenders, usage of Series III EF Extenders lowers AF drive speed to improve AF performance. When Extender EF 1.4X III is used, AF drive speed is reduced by 50%. When Extender EF 2X III is used, AF drive speed is reduced by 75%. This may seem like a drawback, but in reality subject tracking performance remains quite high when Series III Extenders are used with IS II lenses. This is due to improvements in AF precision made possible by the new microcomputer in the extenders. (See http://www.learn.usa.canon.com …ertelephoto_article.shtml
for more info about the extenders and various lenses.)