Personally, I would not run all over the island for gas. Minimal difference between the French side and the Dutch side. Unless it has changed, the Dutch side prices are set by the government. I would advise watching the amount you are paying. Make sure you are not paying the USD amount when the price is in NAF on the Dutch side. This occasionally happens when one does not pay attention. $10 USD would be approx. 18 NAF on the pump.
Some indicate gas is slightly cheaper on the French side but in the grand scheme of things, it is not that big of a deal. Get it when you need it and when it is convenient and try to avoid the weekend as some stations will run out of gas.
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