I can't offer lens specific advice since I only have the 70-200 version I. However, with my version (and all my other long lenses) the 1.4 tc is superb. With the TC20E III I am totally pleased with the results on my 70-200, 200-400, 500, 600. I previously owned the TC20E II and considered it essentially useless. The TC20E III I consider superior to my TC17E.
Do not make the mistake of purchasing the TC20E II!