Aside from the fact that a psych aprn can prescribe medications in addition to therapy whereas a social worker can only do therapy, what else can a psych NP do than a clinical social worker can't.
Is there anything a clinical social worker can do that a Psych NP can't?
Well, the NP does a more medically-oriented evaluation and it's generally shorter in duration, surprisingly, than the initial diagnostic evaluation of a SW. You'll work with biology and examine for medical causes of psychiatric disorders, you'll examine physiologic measures such as ht/wt, vital signs, labs, EKG, brain imaging, etc. And you'll generally refer all therapy to therapists. You'll have therapeutic dialogue with your patients and be credentialed to engage in psychotherapy (with vastly limited training), but the supply and demand warrants your prescription pad as there are multitudes of people who can engage in talk therapy.
The social workers do therapy, the LPCs do therapy, the MFTs do therapy, and the psychologists do therapy. Other than psychometrics and some neuropsych stuff for the psychologists I really have no clue what, if any, of the differences are in the therapeutic modalities of each school of therapy or academic preparation. Granted, CBT is CBT, etc.
If it matters, you'll likely make 2.5-3x the income as a prescriber over a talker. There's actually nothing you'll be credentialed to do as a social worker that you technically couldn't do as a NP (therapy), however, you generally won't be well trained in therapy. I only had one semester of psychotherapy training and frankly have no desire to make a living engaging in psychotherapy. However, I do enjoy helping patients muster their resources, so to speak, and give them a little therapeutic insight.