I'd like to put the focus not on how to heal damage, but the source of it.
If damage is unavoidable (for example, enemies use hitscan weapons), then regenerating health is the way to go about it. Because no matter what you do, how fast you move, and how good you are, you are going to take some damage.
On the flipside, avoidable damage is better suited with health packs, so that the gameplay loop looks something like this "avoid getting hit, since you can do it. If you screw up, go hunt yourself some healthpacks around the map".
Personally, as a huge fan of classic FPS games, I absolutely love the latter approach, since it encourages players to play better, without giving them the impression of doing something wrong each time they get hit by a hitscan weapon.