This is an absolute example of comparing apples and oranges as UF has more applicants on pre-med track than Rice’s total enrolment for whole university. It is less likely to get better support in a huge group, even if they try. Think of it as guidance counselling at a smaller private prep school vs your large overcrowded suburban public high school.
However, it’s much easier getting accepted and affording UF compared to smaller exclusive schools so no pint in comparing two. A right candidate can get into medical schools from any college though it may be difficult to get into programs of their choice or top medical schools.