I just entered Harvard University, not the Medical School, and I will be starting there this Fall.
I go to a US news unranked allopathic medical school in the US. Univeristy of Michigan is top 10 I think, and at that point the difference between Harvard and Michigan is just Ivy league vs non-Ivy league since both have an excellent research and clinical reputation (according to rankings). Thus, I can't imagine it would make a big difference in where you match or anything else in the future. To really assess this, however, look at the match list for Michigan vs Harvard and see where the med students match. Even more so, get hold or a document or ask the matchees if they matched at their top choice. Consider not only whether someone matched but if competitive specialties are matched at: Plastics, Derm, Ortho and Rads, for starters.
Now let me give you my take on the difference between top tier (Michigan, Harvard) vs bottom tier (look at the US News unranked schools). You will learn the exact same material in both schools because there is a national standardized exam process all medical students must go through to do well- the USMLE step exams. Further, you will (or can) use the same review books and have access to the same online resources Harvard kids use: First Aid, Robbins, BRS, Grays- whatever textbook you need to become a doctor you already have at your disposal. The only disadvantage content wise is that top schools sometimes have exclusive learning tools, such as online anatomy dissectors and they also tend to have knowledgeable, dynamic professors who enjoy teaching. Not always, but usually, simply b/c paid professors are happy professors.
Other differences in top tier vs bottom tier mainly involve access to resources: less research projects & less big name researchers, less "high quality = more money" hospitals, and of course a less reputable school name which reduces the automatic value some people will place in you. In terms of medical content and clinical skills, nearly everything you need to know is written in a book or in the minds of your professors, whether they are from a low tier school or not. Nailing down that residency spot will be
mostly dependent on the knowledge you teach yourself (through books, tools, professors) and the skills you learn in school/hospital (through practice, watching others, mentors, etc.). KNowledge + skills are highly accessible no matter which school you go to. I have heard of Caribbean peeps scoring within top 1% of their STEPs and going to become chief of their departments. Learning material and skills is all up to you.
Everything else, namely research, reputation, quality of facilities, name recognition, will hurt you when applying to residencies. I know that even if I score a 270 on the Step 1 and honors alll my classes, the same kid from Harvard with those stats will nail that residency slot over me. By and large though, scores, grades and evals triumph over research. However, the biggest punch you will take it from not having famous/respected professors right you LOR. The best LOR I get from my school will still probably not be as famous or respected as one of the worst LOR from a professor at Harvard. This goes back to name recognition.
In short, most of your success after med school is independent of your med school b/c knowledge (scores, grades) + skills (evals) are mainly dependent on your own effort. Other factors, such as LOR, research, hospital quality and school reputation can hurt you.
Edit: I wrote this post not for you OP, but for anyone searching the threads about this topic so they have my take