Why does AF-ON work better?

My experiences are pretty much the same. O...not really...well not only regarding the use of AF-ON button.

I get much better results ( focus spot on ) when using AF-ON + AF-C ( Continuous focus ) then just "normal" AF-S. That is especially case when using my D800E with 50/1.4G. Using AF-S my "in focus rate" is something about 50% wide open - and when I switch to AF-C  ( I always use AF-ON ) it increases to ca. 85%, maybe even more. Speaking here typically about portraits - focus on the eye - wide open or max up to f2...

At first, I thought something was wrong with my lens, but then it was working fine with my late D700. Then I was about to accept this "36 Mpx sensor easily shows all errors you make - you need to do it better" theory...

But no - that is not the case either. Using AF-C everything is just fine as it should be - just like it was with D700. That is also the case with my 85/1.8G and 105/2 DC.

My conclusion: something is not quite as it should be with AF on my D800

p.s. I did not have the problem with left focus points