There are a few exceptions within a few states. However, in general, the car owner's personal injury protection (PIP) would be primary and the driver's PIP would be excess. Typically, you have to drive the car out of the state in order for PIP to follow you.
Since there are several variables regarding this claim, it being a Florida driver in a Massachusetts car that had the accident while in Main, you may want to contact both the Massachusetts insurance company of the car owner and the insurance company of the Florida driver to determine for certain whose PIP policy should be primary. Normally it would be the MA PIP policy.
According to the Florida insurance regulator a FL PIP policy covers you, the policyholder, and members of your household for accidents occurring outside of Florida but within the U.S. or Canada. Whether this policy will be primary or secondary, excess, will depend upon what the MA insurance company says when they are notified about the accident in ME.