As in undergrads for both. If so then neither will have much difference between them in terms of leading to directly working with people. They are unlikely to provide any practical therapeutic skills at all, undergrads in these areas are primarily just theoretical in nature, and both topics are equally relevant to underlying therories of people/ways of understaning processes. I note you used the "patients", be aware this is generally seen as coming from a medical model, most therapists would cringe/rail against these sort of descriptors. Patients imply a degree of passiveness in therapy, and harks back to dark times where mental health difficulties were seen as primarily biological in nature and forgetting lived experience/trauma in difficulties. Client/people is sufficient, although services do like Service user.
Regarding therapy, you dont need a degree to do this. Some modalities do need all the way up to doctorate (clinical psychologist etc) but some need only practical diplomas (counsellor etc). Regardless of the trg, all require significant self development, insight, empathy and ability to endure significant distress (both in them and you). I say this as too many people think therapy means simply listening and giving advice, it is very rarely ever this.
Greg