FireLance
Legend
IMO, it only makes a difference to the narrative. At the table, it is simply a matter of the DM saying, "You rest a week/a month and recover all your hit points."If you want anything that at least resembles "natural" healing, then you'd need weeks or months to recover from a fight gone bad. Unless you set for a "after one night, all XPs are back" style a la 4E, which is what many people do not like, of course, but that's hardly realistic.
In all other cases you need some sort of "supernatural" healing, unless you want a really really gritty game or a completely different damage tracking system from HPs.
Similarly, in 4e, you could avoid "unrealistic" issues by defining an extended rest as a week's rest or a month's rest in a (reasonably) stress-free environment.