A fixed-back seat has a rigid shell and fixed seat-back angle. It is typically chosen for a firm motorsport-style position and high-rigidity setups.
A recliner uses an adjustable backrest mechanism so the seating angle can be changed without remounting the seat. It can be more convenient when several people share the simulator or when the same cockpit is used for different simulation styles.
The best choice depends on body fit and intended use rather than one design being universally better.