I've flown between the US and Japan on Christmas several times now; never noticed anything different except the occasional "Merry Christmas" from an airport employee in the US. Business as usual in most places in Asia and on Asia-based carriers as Christmas is just another normal day.

Pro is that flights are somewhat emptier than usual. Can't really think of many cons, with the exception of some overpriced airport concessions that I'd never shop at anyway being closed in the US.