So, I think this thread could use a discussion of what different types of health regeneration do in terms of gameplay. Because right now we've got a lot of people shouting back and forth about how it's good or bad, and a lot of people giving examples of games they don't like (or holding up IE games as flawless, which is silly), but not a lot of discussion of how the health regen actually affects the game. So here we go.
Out of Combat
Regenerating: Allows designers to tailor the difficulty of each fight independently, without worrying about the fight before it. This places an emphasis on tactical, rather than strategic, gameplay. At its best, this leads to each fight being exciting and difficult. At its worst, this leads to everything being pitifully easy.
Non-Regenerating: Forces players to consider long-term resource management, promoting strategic gameplay at the cost of making most fights boring (the only interesting one is the last fight before each rest, because that's the only fight where you'll be low on anything important). This also makes it much more difficult to design encounters, as it can be hard to anticipate when players will rest. At its best, this leads to players carefully considering the long-term effects of every combat choice. At its worst, this leads to the game becoming unwinnable because you didn't do well in the last fight and you didn't know there was a dragon in the next room.
It's important to note here that unlimited resting (as was typical of IE games, except in the early game when you were afraid of hobgoblins and wolves, and was most significantly exemplified by Neverwinter Nights) is essentially the same as out of combat regeneration. The only difference is that it forces the player to click a button, which isn't really a problem, but it certainly isn't a strength.
In Combat
Regenerating: Rewards micromanagement (because you can pull injured characters back to regenerate) and reduces reliance on dedicated healing classes. It also encourages some cheap tactics, like kiting, and can make prolonged battles less threatening. It also tends to make back-liners (mages, etc) somewhat more durable than intended, as they don't usually get hit often. At its best, regenerating health allows for some really interesting tactical gameplay. At its worst, it turns the game into a "ring-around-the-ogre."
Non-Regenerating: Makes long battles into epic desperate struggles for survival, and makes every stage of the battle really matter (the goblin that hits you in the first 5 seconds actually does something). At its best, this forces players to be very careful about everything they do. At its worst, this turns battles into a mindless slugfest.
Note that the kiting problem can be solved by requiring characters to stand still and take no actions. This would still allow a character to fall back and rest while other characters covered their retreat, maintaining much (though not all) of the tactical complexity that regenerating health can potentially provide. Of course, you could regenerate while being attacked, but the regenerating would only serve to offset the damage. Think of it as fighting defensively. You only get to regain health while being attacked if the enemy's attacks are so pitiful that they can't overcome your regen (in which case the defense is clearly very easy).
Incidentally, I'm in favor of the system proposed. Semi-regenerating health (the health/stamina system) allows for an element of strategy while making it much harder to get screwed over due to a single fight. In other words, it seems like a pretty good middle ground. In combat regen is very much to my taste, as it matches the "clash and separate" dynamic I experienced in my fencing days, although I do worry about kiting (which is why I proposed the standing still rule, above).
Finally, I just want to say that I'm an old school PnP DM (depending on your definition of old school; I've been gaming for about 15 years, DMing for 10 of them), and I have no problem whatsoever balancing in-combat regen. If the Obsidian folks are half as good at this as I am (and I suspect they're better), they shouldn't have any problems.