If you have a large group and are not always sure if everyone will come, monthly is great. We do that with our team - we have a team building event that is company wide every month. It is optional, so it means that people can come to the ones that work with their schedule. It means we get a different group every month, and everyone gets the chance to do something.
Quarterly is better if you have a small team and you know everyone will be coming every time, You can really focus your budget and scheduling that way as well.