I realize I didn't explicitly answer the question, which is how prestige would impact fellowship applications, but I thought maybe you were missing the point.
So, to clarify (and this has been alluded to earlier in this long thread, so I'd check it out if not already), if you are coming from an obscure residency program and have no contacts with a particular competitive fellowship program, your odds of matriculating there are poorer. If you are from a well known place, your interviewers will have an idea of what your training was like in residency, so your odds of getting into that competitive fellowship will be better. And it's not just that they'll know what your training was like - - they'll consider you to have had better training overall.
In other words, if an applicant from an obscure program and an applicant from a top tier residency are both applying for a competitive fellowship spot, the latter applicant will likely get the spot, all other things being equal. There are ways to overcome this for sure, but we're talking about similar resumes here. Clearly, an applicant from an obscure program with an outstanding application and interview would outshine the resident who had difficulty graduating from a top tier program.
If you're not overly ambitious and plan to stay in a smaller town in community hospital settings without undertaking leadership roles, a top tier program would be of less benefit to your career. This could also be said for mid-sized towns and state universities, where there will be a few individuals displaying varying degrees of reverse-elitism. This is often by parents who don't want to pay for private colleges for their kids, and perhaps feel guilty about that so feel they need to repeatedly denigrate elite colleges. Or, often, their kids can't get into these colleges. Or, also likely, the parents themselves were rejected from the elite colleges. It's amazing how some of these petty phenomena continue into midlife and beyond. It's good to be aware of all this, however, especially as a psychiatrist.
Personally, I do think that overall, the training programs are better at top tier programs, but yes, a lot of that is because those programs recruit many of the top applicants. In lectures/small groups, half of what you learn depends upon what your colleagues pose as questions and/or how they present articles.
It then comes to the small fish in a big pond v a big fish in a small pond. I for one would rather be where I am the norm, but others might want to feel like they're getting more individualized nurturing.
There are certainly many outliers, since some residents will do better where they get lots of individualized attention or free time to read on their own. This atmosphere probably produces really great and not as great products, since there is a larger individualistic component. But yes, I've certainly met my share of residents at "less prestigious" programs who I think are better psychiatrists than many of my colleagues and in some cases, my attendings.
I do think it's critical to have good, compassionate, reliable psychiatrists helping people out in the community, and I completely respect that career path if you choose it. I also think a lot of state universities rock, and there are many reasons to work at one, including that it may be easier to balance academia with quality of life. Whatever path you choose, just please don't become one of those reverse-elitist types! If you do, I fear you will not understand a good number of your patients. And they will perceive it and resent you. And unless it can be worked out in the therapy sessions, the patients will look for another psychiatrist, and perhaps relay to his/her friends that you aren't getting it.
