I think something half way between the best of yester-year and the stuff we have now be the best FPS.
For example:
Classic health meant that developers could give you more survivability, but your mistakes stayed with you until you found a med pack and if you were on low hp the game became impossible.
Regenerating health means that taking an unlucky sniper round to the face will not hamper the overall experience, it also encourages taking cover and tactically retreating but it makes things too easy, especially when the Ai never chases you down (Halo, I'm looking at you).
I believe the best system would be somewhere between the two where your health regenerates, but taking damage lowers your max health. So having a lucky enemy take off 99hp won't ruin the game, but avoiding damage is still rewarded.