RebE, coffee – I think they are both right. b’ Hillel had more integrity in their learning (quoting others first) and, therefore, they became a majority as it was clear to the students that they are not being sold a biased view. Like when some media or posters say something that does not smell right, you either dismiss them, or go double-check and find out the facts that they were trying to avoid…
you can even say – if you stopped by B’ hillel and learned both opinions, presented with integrity, why bother and shlep to b’ Shammai to hear the opinio you already heard? you would do it a couple of times to double-check, but after you confirm that B’ Hillel transmits b’ Shammai correctly, you can as well sit in b’ Hillel and get two classes for the price of one.