To be honest I feel that quite a bit of tension is lost when a regen system is used. Health Pack system games were tense in themselves, and gave you a huge sense of accomplishment for taking out a horde with less than 25% health, while also having slower searches that were rewarding themselves. Regen cuts out the slower parts and subs in more tense situations. I feel it leaves me too... high gear. Too tense, and the accomplishment is gone because I know I can run the same level multiple times the same way and on my last attempt it suddenly works (the first Favela level in Modern Warfare 2 comes to mind, having loaded it plenty of times trying it on Veteran).
That being said, I do enjoy both, but as it stands the regen system is broken as it can be too easily exploited and recovery has no weight on the players experience. The more recent Call of Duty games are too tense and it always feels like you're being carted off to the next mission for more adrenaline straight away. There's always more stuff happening then to feel awesome for surviving. You mow down enemy soldiers like they're nothing. The pacing just feels way off because of this, as there is only one speed: GO! It's the main reason my dad stopped playing FPS games, and why he doesn't want to play Duke Nukem Forever even though he LOVES DN3D and Doom.
Recovery in FPS games should always feel rewarding, as well as in every facet of the game. So does that mean regen health is a bad thing? The way it's used today, yes, but with some alterations it could work really well. I like the idea of a hybrid system but I would make different segments. This might be hard to explain but imagine a health bar at 100%. Now take away 50%. No matter what % health you are on, you will always regen 20% from that point, but no more. The rest has to be healed by a health kit or bandage. If you take over 40% health without getting some regen, you start bleeding out, which forces you to take cover and rest for a bit otherwise you'll take small damage over a period of time, meaning you have to prioritize your healing first otherwise you risk not having as much health. Finally, limbs could be damaged and give bad effects until you use a few bandages, like slower walking, and shaky aiming. I would use this system in Call of Duty as well without the bleedout or bad effects, as it then gives you a priority and reward for prioritizing healing above anything else.
Until that's done, I'm a health pack guy.