Ern-
If the base you are moving to has quite a bit of on-base housing available, you can most likely get a 4 BR house. However, if the base has limited housing available (as it is here at Travis), you have to have at least 3 kiddos to get a 4BR.
Another positive, in addition to what PilotKD said, is that you can keep your house as cold/as warm as you would like without having to pay out the arse in utilities. The last time I lived on base, my house was always a meat locker during the summer months.