It is more nuanced and the "prestige" or rigor factor is typically perceived having much more weight by students then reality suggests. Making it more difficult give any definitive answer, it appears to be vary widely by adcom and seems to be most impactful as the proximity of the undergrad school covaries with the medical school
Boy that a freakin mouthful , wasn't it? Let me try to simplify. These are all general thoughts and observation from interactions with many admissions staff over the past decade at conferences and due my work with OldPreMeds. And my rule of thumb for the vast majority of students is
Take classes at the best institution that you can do well in
1) How you do in courses/GPA is a magnitude or more important compared to where you do your work.
2) For a large percentage of traditional students who have similar backgrounds (ie under 26 and typical biological science majors),"prestige" factor or weighting would seem more a useful tool for adcoms to use across this pool of similar applicants. Nontraditional students, who often have mixed/atypical educational background, it would appear to less useful for adcoms, therefore less likely used and/or less of a factor.
3) Extremely well-known and prestigious schools (i.e. ivy league, standford, hopkins, michigan state) may carry more name recognition and may be used more by adcoms. That is the prestige factor is not linear but seems to be likely taken into account as school's perceived prestige factor increases. But it is likely that a lower proportion on nontraditional attend these schools as their only primary undergraduate course work than traditional students thus not as large a factor as for them.
4) Adcoms vary in the prestige rank given to each school, though likely within similar range or class as well as vary in how weight they give each school in comparison to other factors such as GPA and MCAT. Lastly, there is a large spectrum across adcoms in the "formality" of prestige factor in their admissions process. Some school may include a formal numerical value that will part of an applicants overall ranking formula on initial or early application review that could be used for sending out secondaries or interview invites. This could less formal with more broad categories used later in the application process. Least formal would be use by individual adcom members when either explicitly or unconsciously evaluating an application. In short, the use of prestige factor encompasses a wild spectrum and varies greatly across adcoms .
5) Students may be lured in by the draw of the prestige factor with out consideration for the more highly competitive nature of the student body at the more prestigious institution. For example, in the past year or two there was thread here on SDN by a student going to a good state school, with significant scholarship money, running a 3.8 GPA. He had the opportunity to transfer to Cornell at 4 times the cost where he self admittedly would be able to get a 3.5 . He was absolutely convinced the prestige factor would more than make up for the GPA difference.
6) It is seen that the geographically closer an undergraduate institution is to a medical school, the more likely a consensus accepted perception of the prestige factor is understood by the adcoms and more likely to be used. This has been expressed to me by several admissions officers as they know the school in their own backyard. However my own personal experience in doing a postbacc about a decade ago may illustrate just how important the perception of prestige and rigor plays in the mind of a adcom.
I took organic chemistry during the summer at a somewhat mediocre and small state college taught by a long time faculty member of that school. While he taught this course in the afternoons, her taught the same course, with same lecture, same text, and same exams, at a nearby much larger and very well renown state university research center. He had done this dual summer course setup for both campus for nearly 20 years. While taking the course, I was fortunate to have a meeting with an admissions director from a nearby medical school that is unassociated with either of the above campuses. When I mentioned I was taking the course at the mediocre state college, she someone berated me for not taking the more rigorous version at the state university research center. She was more than a little miffed when I explained that they were exactly the same course, given exactly same exams, and taught for nearly two decades by the same professor, who was faculty at the smaller college not the research center. Additionally this small state college had 3 summer terms (started the weekend after spring term and continued until the weekend before fall classes). In the last term following the 2 organic courses, some student were going to take biochem in the last 5 week term. When I mentioned this to the admissions director as well she completely dismissive of this. When I informed her it was being taught by a well-known faculty of a state medical school, she was beside herself. I would up getting emails sent from the organic chem faculty member as well as the biochem faculty (who apparently used his summer teaching stint as personal recharge after being in the lab the other 10 months of the year) to the admissions director.
So what is a nontrad to do with all this info? As I said at the beginning of this , with the many factor and issues that nontrads have to deal with and the balances and compromises they may have to make in order to complete prerequisites, my rule of thumb is
Take classes at the best institution that you can do well in
