Orange Beach has a short public shoreline compared with the length of its condominium wall, so the accesses matter and they are not interchangeable.
Cotton Bayou is the all-rounder. Ramped access, matting, restrooms, showers, a lot big enough to be worth driving to. If you have a stroller, a wagon, a wheelchair or a group, start here.
Alabama Point, a couple of miles east at Perdido Pass, has far more sand per person and the rock jetties to look at, plus a free life jacket loaner board. It is the better beach and the worse car park.
Romar Beach, west of here, is smaller and quieter, and works well if you are already staying within walking distance.
Gulf State Park's own pavilion and pier accesses sit further west again in Gulf Shores, with more infrastructure and correspondingly more people.
The honest summary is that Cotton Bayou is the access you choose for convenience and equipment rather than for solitude. If what you want is an empty stretch of sand, drive west to the Fort Morgan peninsula instead and accept that there will be no restroom when you get there.