That's actually a very good question!
Rarely have they played each other in the regular season, since they play in different leagues. The only times they could have met would have been during interleague play, which began in 1997.
If I had to take a guess, it would be that both anthems are played, since the majority of players are from the U.S., and MLB is essentially a US-based organization. (again, just a guess).
I'm sure they've played in the spring training, but those games are in Florida, Arizona, etc.
Kevin