Verified answer

Long Beach is more accessible. It's in a middle of town and there is LIRR station just a few blocks from the beach.

Fire Island is more secluded. There are some beach bungalow communities, but they are accessible by ferry. No cars, as there is only a single dirt road. If you walk along the beach, away from the beach bungalows, you can have the whole beach to yourself. There is Robert Moses Park public beach on the west end of Fire Island, but on summer weekends traffic is is terrible. If I go there, I go during the weekday. Just east of the Robert Moses, in front of the lighthouse, is the nude beach.

Of the two, I prefer the Fire Island.