No doubt, this is a controversial topic.
Traditionally, HBS has had the highest yield (88-90% range) of all MBA programs, followed by Stanford (78-84% range).
(Yield of an incoming class of an MBA program is the percentage of accepted applicants who join the program, and it’s one of the best market-driven statistics that reflect reputation of a program.)
Then, how does such bold, cold statistic lie?
It doesn’t.
But it doesn’t reveal the entire picture, either.
(Note: Admission policies of schools and guidelines for standardized tests can change. Refer to their website for the most updated information.)
Stanford’s yield is qualitatively better
Let’s scrutinize the admission data (class of 2015) for the two schools:

Note: Numbers in black have been inputted, whereas those in red have been computed.
Source: Admission data and number of dual admits
What do percentages in the last row tell?
Stanford competes one-to-one with HBS, its closest competitor, for a whopping 31% of its accepted applicants, and with other schools for up to 69%.
Whereas, HBS competes one-to-one with Stanford for only 14% of its accepted applicants, and with other schools for up to 86%.

It’s a common knowledge that Stanford and HBS are the two most popular MBA programs, and that they compete mostly with each other to attract the dual admits. Having said that, as per the data above, HBS faces relatively less competition in retaining its accepted applicants: it competes with Stanford, its closest rival, for only 14% of its accepted applicants, and with relatively easier competitors for up to 86%.
Under these circumstances, isn’t 84% yield of Stanford qualitatively superior to 89% of HBS?