I ran some numbers like this a couple of years ago, based on a) some hand-wavy estimation of what the personal loot percentage chance was (may have been from a blue) and b) my horrible understanding of the mathematics of expected value, and the answers that popped out was that in terms of EV(pieces of loot), personal loot won out, and it wasn't that close. ISTR (and please dont trust my memory on this) that the personal loot drop chance was something in the 20-30% range.
That did - obviously - depend on a number that was fairly hard to peg accurately, so as always, YMMV + ¯\_(ツ)_/¯
The one thing that I really wish that Blizz would do (and I've tweeted at them before, with no response) would have personal loot award tier tokens, rather than actual tier pieces, which would (IMO) help address the issue of better distribution of tier gear within a raid.