I don't think there's a specific way to gauge this. Many medical schools have multiple staff teaching behvioral sciences, have many hospitals which offer pyschiatry rotations & electives. So its hard to say which is the BEST.
I would take a look at which teaching hospitals are the noted to be the best and see if they are connected with specific medical schools. That way, as a student in that school, you have a reasonable chance of being in that hospital as a student.
This is the only approach I can reccomend that has some structure to it, and I don't even think its a good one. The information you need to take in is at a much more basic level than what most programs who have a reputation for excellence emphasize. For example most highly reputed programs are such because of their research achievements, yet research if anything will have little to do with your training in medschool in psychiatry or the behavioral sciences.
My own residency program which is the COOPER/UMDNJ program located in Camden NJ is a part of the UMDNJ Robert Wood Johnson medical school in New Brunswick & takes their students (yeah I know, they're over 1 hour apart from each other).
My program has a good reputation for teaching, but for research is on the up & coming side, so all in all its not one of those high reputation programs yet it has one of the highest rates of students who go through this program who end up wanting to do psychiatry because they say they liked their experience with the program. I know I did. My experience at Cooper significantly augmented my already strong desire to be a psychiatrist and I put Cooper high on my match list for that reason even though I was interviewed at other programs that I knew were considered more prestigious.
Just getting into medschool is tough and I would focus on just getting in at this point, not on which school is better for psychiatry. Should you get in, most schools have multiple hospitals where you can do your rotation in psyche. Best way to approach that is to ask students who've already worked in the various hospitals what their experiences were with the specific hospital & choose the one they thought was the best for teaching psychiatry.
