I find the concept of busy beavers to be extremely interesting and disconcerting because of their surrounding concepts and their baggage.
So BB (10¹⁰⁰) is interesting not because it's large or small but because of the mind-boggling complexity encodable by turing machines with that many states, or that the value of BB (10¹⁰⁰) is so absurd we can't say exactly how big it is without also incidentally saying things about whether ZF(C) is consistent (600 states is already enough to trigger this).