It all depends on the school. You shouldn't compare how much you "get" and instead should compare how much you take out in loans when comparing medical schools (because of tuition variability and living expense variability among schools/locations). Most top medical schools are moving towards the use of the "unit loan" model. The unit loan is the amount of loans you MUST take out before grant aid kicks in and covers the rest. Usually the breakdown is : Total COA = EFC + Unit Loan + Grant Aid . Again, you must take out the full amount of the unit loan to be eligible for the Discount/Grant Aid/Scholarship/Free money from the schoool. The way it works is that the students with the lowest EFCs also have the lowest unit loans and receive grant aid to cover the rest. At some schools there are even special scholarships awarded to some students which cover a portion or even all of their unit loan. However, for most students, the unit loan amount you are offered (above the minimum) has some correlation with your EFC amount (when EFC is not zero).
Since you are postulating an EFC of zero then we will be talking about minimums. Which means you should look up each school you are interested in, read their financial aid policies, and discover what that school's minimum unit loan is for whatever entering class year you plan to be. I spent a few minutes googling this myself and found some examples: Harvard's is 33k. Cornell's is 32k. NYMC's is 33k. Mount Sinai's is 31k. Again, these are minimums and you will only qualify for those levels if you have a very low or near zero EFC. Some friends I have who are in private medical schools with middle income parents have unit loans in the 40's. And some of them in reality take out more than that because their parents do not give them the whole EFC.
Another important variable is the breakdown of loan types in these unit loans. Most of these packages include the max in federal loans you qualify for (rates and terms/conditions usually are the same nationwide). But many top schools offer significant amounts of institutional loans which have better rates and terms/conditions than private loans or federal loans and will use these funds as a significant part of your unit loan. Some schools will only offer you high rate loans to cover the difference if you go above the unit loan (ie borrowing for part of an EFC that your parents do not pay you). While other schools have more reasonable options of extra institutional loans for this need. Loan types is an often overlooked variable that is more complex than just an absolute number of the unit loan amount and is something that requires careful consideration. In general, the better the school you plan on going to, the better these loan options are.