I recently had some unplanned cash at hand and upgraded the 4 IS to 2,8 II IS.
Although pretty much razor sharp, sometimes the 4 did limit my exposure time - I know ...this is post-hoc rationalizing for GAS
I really see a difference in autofocus performance on my 5D3, and I can make good use of the additional weight for training purpose...
Bottom line: If IQ is your driver, 4 will get you there. If weight and shooting time per day may be a limiting factor, don't go for the 2,8. It is substantially heavier more than double the weight and very obvious (no really for candid portraits)
If you are strong and committed to weight lifting -go for it, it is sooo cool...
With the 4 you have no room for extender. It's f8 and bump iso or f8+ and MF. 2.8 leave you much more headroom.
The faculty to be useable with a x1.4 or x2 is a point to consider (what's not to love in a good 140-400 f5.6 for 400 bucks? -once you already have the lens that is-)
I've used a 70-200 f4 LIS with a 1.4x many times. It becomes an effective 100-300 f5.6 LIS with simular optical charectoristics to the new 70-300 f5.6 LIS. Sure, if you want to use a 2x tc you will need a 5DIII or 1Dx and only the centre points will work....but even with the f2.8 LIS II version, the 2x is pushing it a bit and the AF is pretty slow and ponderous.