Most places have the first one on scene be "in control" until the situation dictates otherwise. In this case, the FD would be in charge due to the extrication. EMS would essentially tell FD what they need to do for the patient before/after extrication and FD would usually work around those recommendations. The captain or battalion chief is in charge, usually with a paramedic coordinating EMS while the Capt/BC does the fire/extrication side. There's all sorts of flow charts.

Cops usually go back to traffic/scene control as soon as FD or EMS show up.