Sigh, are we going to have this discussion again? If the player can, for example, aim better/faster/more accurately you can design the levels differently and have different speed of player/camera movement.
Aiming better is more about player's skills then frame rate: a poor player is poor at 60fps as well as 30fps.
Faster aim/camera has nothing do with frame rate: if max acceleration is set at 50 it's not like it will magically go up at 100 just because you are playing at 60fps.
Accuracy has more to do with sensitivity than frame rate as well.
Level design is more influenced by RAM than frame rate.
Character movement speed has nothing to do with frame rate: you can make a slow character even at 60fps.
Detail, input lag and image fluidity are influenced by frame rate.
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