As far as med school, you can get into med school from either one of them. According to the AAMC, the schools produced the following number of applicants to med school in 2015.
Florida: 802
Miami: 373
https://www.aamc.org/data/facts/applicantmatriculant/86042/factstablea2.html
Keep in mind that UM is a much smaller school.
The average rate of med school acceptance is 40%, and I would expect that these schools are probably near the national average, and I would suspect that opportunities are likely equal at both.
If you are interested in how UF or UM graduates do at schools like Yale or Stanford, you can do a websearch for med school admissions. Here is Yales class (starts on page 211). It is probably too small of a sample size to mean anything, but out of around 100 students, it looks like there were two UM grads and two UF grads in the 2015 class of MDs at Yale.
http://www.yale.edu/printer/bulletin/htmlfiles/med/school-of-medicine-2015-2016.pdf
However, the vast majority of students at Yale attended other Ivies or other top 20 ranked schools like Johns Hopkins, and most successful med school applicants from schools like UF or UM likely attended in-state med schools. Unless you have a strong preference for one over the other, I would go with the least expensive option. Good luck!