From someone who interviewed at both these places and without actually experiencing it firsthand (well except I did an away rotation at one of these programs and had some direct exposure), I can give you my impression from the interview day regarding psychotherapy since I also want a program with strong quality and breadth of psychotherapy training.
UCLA-Semel is the king of outpatient psychiatry in all of California. They have an unbelievable amount of specialty clinics dedicated to almost every type of psychiatric disorder, patient population, and therapy type. In terms of clinics, they also have an anxiety disorders clinic, partial hospitalization program, OCD outpatient day program, Intensive Short Term Psychodynamic Psychotherapy Clinic, Eating Disorders Clinic, Women's Life Clinic, VA HIV Clinic, Psycho-Oncology Clinic, Post Deployment Clinic, and many many more. The psychotherapy modalities you have access to include the standard dynamic, interpersonal, CBT, supportive, DBT (although Harbor-UCLA is probably stronger in this), parent training, family therapy, motivational interviewing and brief psychotherapy, but they also have the less common ones such as hypnotherapy, dream analysis (is this for real?), mentalization, ISTDP-AB, couples therapy, sex therapy, and any of the psychoanalytic institutes in LA (NCP, ICP, PCC, LAIPS, Jung) as well as the 450+ private practice faculty affiliated with UCLA (the Psychiatric Clinical Faculty Association). Psychotherapy cases are required in PGY3 and consist of at least 2 patients, one in CBT and the other in Dynamic with at least 42 sessions in this year. This is not including the 2 half days you have off in PGY3 to do whatever you want, and 3 half days off in PGY4. However, 50% of residents start in PGY2, and some start in PGY-1 as long as you can find a mentor which isn't difficult at all. There is therapy for both adult and child although the adult psychotherapy is much stronger. In terms of quality, residents are supervised through a one way mirror by a faculty member during psychotherapy sessions, and if you aren't seeing patients in that way, then many residents will record their session and review them with psychotherapy faculty, which I believe is the best way to get better at psychotherapy is to have someone give constructive feedback on what you're doing right and wrong during your interview.
NYU will also offer you excellent training in psychotherapy, although I got the impression that some of the other NY programs were stronger. Given the volume of psychiatric care at NYU, they have an incredibly high patient population in every setting - VA, Public, Private, small city clinics, state hospitals, and prison. This obviously gives you exposure to different psychotherapy skills than being at just a large academic medical center like UCLA. They claim to have every type of therapy, including the common ones psychodynamic, cognitive, supportive, brief, and dialectical behavioral therapies, and the less common ones such as sex therapy and transference-focused psychotherapy. I don't believe they have mentalization, hypnotherapy, ISTDP, or family therapy, but I could be wrong. There are master's classes where they bring in someone who is an expert in psychotherapy and discuss cases, watch videos, and teach residents about different types of modalities. Many of the residents record their psychotherapy sessions since the residents can have their sessions at Bellevue, Langone, Washington Square, the VA, and several other clinics. NYU definitely does not have the same number of specialty clinics that UCLA does, nor do they offer as many electives. They have the Institute of Psychoanalytic Education as well as many other psychoanalytic institutes in NYC (NYPS&I, APA, MIA, ICP).
Overall, I get the sense that the psychotherapy training at UCLA has more breadth and depth than NYU, but there is definitely less of a tradition of dynamic-oriented faculty at UCLA than NYU so the training will be a bit more formal versus in a more casual supervisory meeting. In the end, I think both offer excellent psychotherapy training. If you're looking for psychoanalytically-oriented faculty, then historically it was Cornell > NYU > UCLA, but that probably means little in terms of the quality of psychotherapy training, which I think depends more on the residency schedule structure, early exposure to cases, number of sessions per patient, type of supervision (directly watching vs video review vs indirect case discussion vs no supervision), and number of hours faculty coaching and giving constructive feedback on resident technique. This is just my impression so take it with a grain of kosher salt.
