A dedicated cinema has to decide what stays constant as the aspect ratio changes: image height, image width, or neither.
Constant image height
Constant image height is closely associated with wide CinemaScope-style screens. Wider films expand horizontally while image height remains broadly consistent. This can create a very cinematic relationship between flat and scope content.
Constant image width
Constant image width keeps the horizontal dimension fixed, so wider aspect ratios become shorter. It can simplify some room and screen constraints and may suit systems where available width is the limiting factor.
Masking makes the choice visible
A masking system can physically frame different image shapes and materially improve the finished presentation. Two-way and four-way masking solve different requirements.
Decide before procurement
The screen format affects projector lens memory or external processing, screen dimensions, loudspeaker placement and seating sightlines. It belongs in the initial design brief, not at the end.