Long Bay stretches along the eastern side of Big Corn and is a different animal from Picnic Center. There is no tourism infrastructure to speak of, the surf is rougher, and the wind from the Atlantic side comes in steadily. What you get instead is space — a long curve of sand that you can have largely to yourself even in high season, with a few local fishing boats pulled up at the south end.
Swimming is fine but mind the current on windier days. The road around the island runs close behind the beach, so it is an easy stop on a circumnavigation by bike or scooter. Bring water and a hat; there is no shade and no shop close by.