I'm a Longwood resident, and I agree almost entirely with sopsyched's assessment. Here would be my caveats... first off, "strong psychotherapy training" is present at all 3 programs. Each of the 3 pay far more than lip service to teaching and training in the various modalities of psychotherapy, and each of the 3 have many, wonderful supervisors ranging from analysts and existentialists to DBT and CBT specialists. If you want to be the best psychotherapist that you can be (after 4 years - which is a ridiculously short training period in psychotherapy), you cannot go wrong with any of these programs. So, I wouldn't agree with the statement, "If strong psychotherapy training is a priority for you, ... Cambridge is the best of the 4." And I'm not taking ANYTHING away from Cambridge - it's a truly special place, and the residents there do seem to love their experience.
A clarification about research... there is important, well-funded research in both the basic neurosciences and in the more clinical aspects of the field going on at Beth Israel and Mass Mental Health Center (both part of Longwood). Also, anyone who is thinking about coming to Boston should keep in mind that ANY research lab in the city would love to take on an interested psychiatry resident - why wouldn't they!? We're a relatively-knowledgeable source of free manpower (or womanpower) who knows how to work hard. My research advisors at Longwood know all sorts of top people at McLean and Cambridge and Boston Medical Center (BU), and they're more than willing to call their contacts at these places if my interests take me in these directions. With all of the faculty moving from one place to another, it's not nearly as territorial as I was led to believe when I was applying to programs. That being said, at my program, in particular, it's rare for a resident to publish significantly in years 1-3 because the clinical demands are so high (NOT because the opportunities are not there).
All in all, I echo sopsyched's statement that the residents at these programs very much self-select. I'd venture to say that at least 90% of the residents at each of these programs had their respective program ranked #1 going into the Match (and this happens at a number of non-Harvard programs as well, I should add). There's no clear consensus as to which is "the best" - you just have to go interview and see where you feel most comfortable.