I think they're right, it's not a competition as is the football game, even though both bands really want to do their best to out-do the other, band parents and their fans at most places are very respectful and appreciative of the other bands.
I would pose the question opposite, which place is the greatest place to play as a visiting band? Facilities, seating, logistics, laison to the other band, concession bennies, crowd appreciation, you name it. Who makes you feel welcome?