I think they care about all the things you mentioned, especially LORs from people known in the field, AOA, lots of honors, etc. There is a strong global health vibe, underserved health vibe, etc. I think they care about ECs a lot. Research is good, but I think a clinical/public health research angle is better than a basic science research angle. That's in contrast to categorical medicine and pediatrics, where basic science is often highly valued. With the possible exception of BWH-BCH, I don't think the programs are terribly hung up on school name in whom they match (of course, that may have to do with how far down their list they go). They may bias for big name med schools in inviting people to interview, but I see people from a wide range of medical schools at other top programs like MGH, Duke, Penn, JHU, UCLA, etc.
Also, med-peds itself tends to be a bit more about "match" than just prestige, since it is infrequent for a program to have extremely strong medicine and extremely strong pediatrics. In fact, I can think of only three (won't name them here) where both categorical programs have a very strong reputation, one of which has some bizarre priorities and sees itself as more of a family medicine/inner city medicine program than a standard med-peds program. Most programs are stronger on one end than another. Some are markedly lopsided (e.g. Cincinnati for pediatrics (weaker medicine), MGH for medicine (weaker pediatrics), etc.). And some have a strong reputation because of logevity, experience, and reputation as med--peds programs, rather than categorical program reputation (e.g. Rochester, UNC). So in the end it's more about personalities, fit, what you're looking for (research opportunities in basic science vs. public health vs. policy), location, and - in many cases, whether you're a little more of an internist or a pediatrician at heart.
