Where are you staying? This may influence your decision. I have rented cars multiple times. Downtown Philipsburg is almost always busy and is certainly very crowded whenever there are cruise ships in port. Parking there is always tricky. Just go two-three blocks away from the beach and you will be fine. The other problem areas are around the two lift bridges (Simpson Bay and Marigot), however Simpson Bay is less congested since the new causeway/bridge opened. Parking in Marigot is easy.
You are planning to visit Dutch and French sides. That suggests some longish distances and some good hills for which a scooter may not be the best choice. Also, with a rental car, you will not need a taxi to get back and forth to the airport.
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