Warning: gratuitous name dropping
I have family that are PhD (Harvard), MBA (Chicago School of Business), Law (Duke), Law (Georgia), Broadcast Journalism (BYU), MS of Economics (BYU)...etc. That's just my sister's kids. We have engineers from MIT and Brown, musicians from Eastman and Julliard, PhD (Math) from Berkley and USC, and a slew of medical doctors and dentists from all over...including (ugh) the yewts.
It is my opinion and ONLY my opinion (after many conversations over the years with various family members), that Stanford is harder to get into than Harvard...and that a full ride to Stanford is extremely rare. At least on the academic side.