I said both, but it really does depend on the game. I just couldn't see regenerating health work on games like RE5 or Left 4 Dead. Actually Left 4 Dead is by far the best example of being as realistic as possible with health management.
Regeneration works great for war games like Call of Duty where so much is flying by your head.
Then you have the system that works great for that particular game and works ideas around that. Like how in Crysis you have regenerating health because your nano suit has the ability to heal you (also like Halo). Games like Quake or Unreal Tournament also work great with a Health Pack since you also have things like the Keg-O-Health and what not.
My favorite health systems have to be in games like FarCry 2 (allow you to take hits, but if you take a critical hit you need to heal yourself), Left 4 Dead (as you take damage you move slower and slower until you either heal up or take some temp Pain Pills) and even MoH: Airborne which uses the 3 bar health with regeneration for each bar. FarCry 2 basically took this a step further by making you do surgery on yourself. I even like that when you die you are not actually dead and one of your friends will save you. Adds a hint of realism cause I don't actually like to die

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Also I find that with Health Packs I actually do more running away or taking cover than with regenerating health, so I guess it's different with me.