Yes. Depends on the cause of pain. Depression causes the perception of pain to be worse for the patient. The major classes of antidepressants are: tricyclic antidepressants, selective serotonin reuptake inhibitors, serotonin and norepinephrine reuptake inhibitors, norepinephrine reuptake inhibitors, serotonin receptor modulators. Your doctor will have to sort out which medication is right for you.
No. There is no yes/no, "better than", "as good as", as your treatment should be individualized for you. However, all of the antidepressants whose action is to block the re-uptake of a chemical which transmits nerve impulses called norepinephrine are preferred over other antidepressants for use in pain control.