I've yet to find a game where a 3D portrait looks better graphically, shows a better expression or gives a better overall impression of the character than a hand painted portrait.
Agreed. Now, if they were animated portraits, then sure, maybe 3D would do best. But just a still shot to capture a character's... ehh... "essence" sounds really artsy, but essentially that for lack of a better word... 2D cannot be beat, as you're purely creating the image for that one shot, and not creating it for full 3D animation.
Man... how cool would it be to get animated sprite portraits like the main character (what's his name... Blastowitz?) from the original Wolfenstein 3D? You know... the more damaged he got, the more it showed on his portrait. And he cringed when he got damaged, etc. Hehe. Infeasible, I'm sure, but that would rock!