PhD programs of medical school
In general, the biggest difference between PhD programs at med schools and those not at med schools is simply their research focus. Often they have differences in the administration and faculty associated with the program, but at least for Harvard (that's where I just finished my PhD), the difference between the med school programs and those not at the med school is probably smaller than the difference between Harvard's med school programs and Stanford's med school programs.

Each PhD program is different, and may have different requirements in terms of admission and selectivity, but for the top tier of graduate schools, the difference is probably not hugely noticeable. There are also likely to be differences between say the Immunology program at Harvard and the BBS program, even thought they're both at the med school. 

I can't speak to Stanford, but at Harvard, your GPA and GRE's will have some influence, but your research experience and letters of recommendation will hold far more weight. 

I'd say, apply to the programs you're most interested in, and then if you're invited to interview, make your decisions after you've visited the schools. You want to base your choice on the feeling you get from the students and faculty - different programs align more with different personalities. If you're choosing between Harvard and Stanford, you won't be choosing between different qualities of research (both institutions are phenomenal), you want to go where you'll be happiest because of culture etc. 

Edit: Spelling