Treat them as two destinations that happen to share a car park.
The Gulf side faces south-west into open water. It is the wider beach, the better one for swimming and for lying about, and it is where the shell line forms. It is also where the afternoon light lands, though the point itself is oriented east, so proper Gulf sunsets are better watched from further west along the island.
The bay side faces north-east across San Carlos Bay towards the causeway and Punta Rassa. The water is flatter, the beach is narrower and shellier underfoot, and there is usually current running past the point. It is the better side for watching birds work the shallows and for the sunrise, and it is where paddlers put in.
The boardwalk between them runs through mangrove and coastal scrub and is the quiet part of the park. It is short, it is shaded, and it is the only stretch of this site that feels like the island's interior rather than its edge.
If you have a couple of hours, walk all three. Most visitors see one and drive away.