Well, if you add weight to pushups such as a weighted vest, then it's no longer a bodyweight exercise. The problem with doing pushup variations is that they are often harder because they work different muscles than a standard pushup. Handstand pushups work the shoulders instead of the chest. They are akin to a military press. Pike Pushups are more like an incline or decline bench than a standard bench. A one arm pushup is akin to doing a bench press with both hands in the dead center of the bar. Not a good position to put your wrists in, and it works your triceps almost exclusively. The wider your grip the more your chest is involved and the narrower your grip the more your triceps are involved. Rings are a great way to figure out how to get external shoulder rotation (bending the bar cue) but don't add more weight to the exercise. Archer pushups are like a pec fly, which is great, but definitely not something to make the main focus of your chest routine.
I already know low rep, high weight gets greater strength results hence the weighted push ups. You were comparing bodyweight push ups vs Bench Press, but I wanted to give more options for building strength over endurance. Calisthenics can use weights too.