I think sandbox is a more fun way to create your own story, but it has potential issues. Many lords have special Items, King Stannis and his sword, King Renlyand his armor, the Khal and his arakh and a number of other lords. If their factions are overrun in sandbox mode and they leave the realm, you lose the chance at acquiring this weapon (by executing or sending them to the wall), if Joeffery is defeated in battle and escapes prison or defects in sandbox, you may lose the chance to recruit the kingsguard. These are cool little things you can do which are more secure when in static, but i still think that sandbox has the unique experience of seeing which factions die and win , and it uniquely shapes your own world.

TL;DR
Static wars make factions less likely to be eliminated and that allows for the aqcuisition of cool items and companions, whilst sandbox creates a more unique world in my opinion.

Thanks

Follow up question to this.... does static default to sandbox when the main quest lines are done? How does everything wrap up?

I've never finished all the main questlines, so i am not sure. But you can turn static wars off in-game if you chose it, but you cannot turn it back on.