There is no significant difference between Harvard and Yale, and what is offered, or expected, of students interested in pre-med courses.
That said – and I’ve posted this elsewhere – it’s very difficult to get an A in some pre-med courses at HY, and some students interested in pre-med may actually be better off attending another college that has less rigorous standards.
For example, last semester my daughter, who just graduated from Harvard, took LS2, which is one of the courses Harvard students thinking of going to medical school take (http://www.registrar.fas.harvard.edu/courses-exams/course-catalog/life-sciences-2-evolutionary-human-physiology-and-anatomy).
However, as it’s Harvard (and this occurs at Yale as well), the course was jammed packed with things you wouldn’t be asked to do at another college, like identifying every bone in the human body by week two in the course, something my wife didn’t have to do until medical school! Yes, it’s a fabulous experience, but because HY professors have higher expectations of their student’s, few students actually get A’s in the course. So, another student coming out of a flagship state college, which doesn’t have as high expectations or the resources of HY – read $$$ – may have a higher GPA and be in a better position for medical school than a student coming out of HY with a B or a B+ in a course like LS2. Ditto with other pre-med courses at HY. Fortunately for my daughter, she got an A- in LS2 and was happy with the grade, as the course was the most demanding course she took in her four years at Harvard (and this is coming from a student who graduated Phi Beta Kappa). So, whatever school you ultimately choose, you should go in with your eyes wide open.