Yes if you appreciate better resolution. I was doing some AF Micro-Adjusting yesterday and we compared the resolution between these 2 and it is noticeably better.
I believe it will also autofocus faster with certain newer lenses like the 70-200f/2.8L II IS and the II Super Telephotos. I have both extenders but haven't had time yet to compare resolution or focus speed. But it does seem autofocus with the 70-200f/2.8L II IS is very quick with version III.
VERY very small difference in favor of the Mark III in the center. You barely see the difference at 100% even when looking closely. Anywhere near the edges at all, the Mark III is noticeably sharper though. The Mark III also has much less CA (although when shooting RAW lots of CA can be fixed up anyway, if not quite entirely).
If you have an IS Mark II super-tele then it apparently makes the focusing more accurate. I don't have any IS Mark II super-tele though, so I can't say how it works out in reality.
Only you can decided if it is worth it. I did end up keeping the Mark III myself, although I'm sure many wouldn't find it worth it.
I have the Mark II's that cost me about $200-$250 each, two or three years back. I seldom use them, so upgrading to double the price is not for me. I've even considered getting Kenko TC's so I can use one on lenses like my 100mmL which does not work with Canon TC's.
With the 1DX being TC unfriendly (meaning it won't AF on many common popular lenses with a TC when the refulting aperture is f/8), I am reluctant to spend more money on TC's until I see if the 1DX specs are changed.