This is asked on the forum frequently. Most bang for your buck fellowship is child, followed by addiction/forensics. Sleep is also mentioned, though lately that field is suffering somewhat on the reimbursement side. However, if you do any of these fellowships for money it'll be pretty stupid. A lot of child trained psychiatrists don't do any child. A lot of child psychiatrists get paid squat for working in public settings.
Depending on what type of applicant you are (i.e. top school/top grade etc) vs. average vs. lower tier, psychiatry residency placement often has more effect on salary, though even that intuition comes with lots of caveats. The main difference in psychiatrist pay is ownership structure and schedule. I'd say as a run of the mill applicant, choosing the two fields (psych/anesthesia) based on pay would be unwise, because if you work the same amount the pay may be similar. At the high end, I think high end cash pp subspecialty psych is much more of a lifestyle specialty than general anesthesia (have good friends in this field), even pain (which is in itself considered more lifestyle within anesthesia). Group pain practices, for example, often require call. Though I suspect the ceiling is higher in pain--kind of like derm has a lower ceiling but is probably more of a lifestyle specialty than pain.
As a general rule in medicine, highest ceiling salaries deal with procedure specialties that carry high overhead/facilities fee/ownership and passive income (large teams, larger billings, etc). Best lifestyle specialties deal with very small niche populations that are usually well off and small clinical teams.