I voted for the second, but I want to clarify that by saying I think everyone should have some healing capability. Those who dedicate themselves to healing, however, should have auxiliary reserves of healing ability beyond what a normal character does, and should probably have the ability to heal creatures other than themselves reserved. Also, healing shouldn't suck, but meh.
Oh, and the Heal skill should be able to heal HP and, with a sufficiently high check, ability damage. Pending a sane skill system, obviously.