In my opinion, the Top Psychiatry program should be defined as the program where you gain the ability, having gone there, to have no restrictions in achieving your professional goals after residency.
For some people, this is quite specific...like wanting to practice in a certain location..and thus, a regional approach, which you can see even in the residents in big academic institutions, leads people to the relative "best" program for them.
Similarly, if you know you want to do research in a certain sub-field of psychiatry, like Addictions, Neuroimaging, etc...then you can find programs where the leaders in those fields have little empires that you can latch onto, which therefore will give you the fast track to success as being on the front line of the best research and benefitting from being a "disciple" of so and so expert.
The real test of a program though, is if one is unsure of where they want to end up in psychiatry, but they know they want to have every option available to them in residency to pursue whatever sparks their interest while they are training. Whether it be working with a special clinical population, doing research, fellowship, or private practice as a generalist, the TOP program, should not disadvantage you in any of the options.
Thus one can't ignore "name recognition" in this equation, because certain programs are assumed to provide excellent education due to historical factors. Ivy league names tend to get the benefit of the doubt in this area, none more than Harvard. It is without question, that training at Harvard is something one can use to their advantage academically, but actually I would say moreso in the private practice world. The lay public eats that stuff up. But remember, most places tied to reputable undergrad universities tend to get the benefit of the doubt, and this bias is amplified in the local region for those universities.
However, being able to go to a program that offers exposure to various parts of psychiatry in the best combination of "breadth and depth" to me is the best program. That generally eliminates non-university based programs because of research and specialized training and "thought leaders" in the field all being tied to these places. Some people say "I'm not interested in research" and then discount programs with big time research dollars and instead look for "clinical" programs. I think that is a big mistake, because the research is usually tied to specialized clinics and experts that are a few years ahead of the curve of what is happening elsewhere clinically and one can really gain an advantage for their future by being at those places.
In fact, the field is so in flux, that even if you are at a great clinical program where you see lots of patients and have good teachers, its hard to feel confident in what you are learning, because so much changes every year, that so much of what people are teaching you ends up being completely wrong.
If I were doing it over again, I would look for places that really had big time research in multiple areas and offered most or all fellowships. I would not go for the most volume heavy place, but also not the easiest program.
I really think the research happening at a certain place matters a heck of a lot more than medical students give it credit. And this includes psychotherapy research.
So looking at NIMH and other research dollars gets a bad rap, but as I've reflected on my training as a graduate, I realize now (as a total non-researcher), that research being done at the institution has such a ripple effect on the entire residency experience.
Thats not to say you can't get excellent training at a hundred different places, but if you are talking about the TOP programs, which are few, then this is what I would say...and I think it doesn't linearly translate to what is the "most competitive" program to get into because so many people prioritize regional interests (understandably so) over actual training interests.