I honestly believe that loaded ring push-ups are better than bench press for non-strength athletes (e.g. team athletes). At least it is the first option after bench press and it is truly excellent assistance lift for upper body [horizontal] push.
Using rings forces you to use shoulder stabilizers more and allows for ‘natural’ movement of the scapula, and also allows shoulder rotation which can allow lower joint stress [penalty] compared to barbell bench press. Since the stability is compromised, the load used will probably be less than in bench press, hence bench press should still be performed to provide an overload [depend on the athlete need to upper body push strength]. Besides, it is a great core workout as well since you need to stabilize the core and prevent hips from sagging down under load.
Short, semi-related rant…
The worst upper body press exercises in my opinion is incline bench press. Here is my rationale. To be a good bench pressed one needs to provide stable platform to press, and that means pinching the shoulder blades down and back. This works nicely for flat bench press, but one still needs to perform push-up variations to allow for natural rhythm. This rhythm is very important in vertical/overhead pressing and without it shoulders experience greater penalty. In inclined bench press you shoulder blades should still be pinched down and back, but the arms more slightly overhead. Besides, a lot of guys are arching during incline, but compared to flat bench press where there is no ‘axial’ load on the spine, there is some during incline.
I know that I might stir some debate on this, so keep in mind that this is only mine opinion. I also wonder why some coaches like Mike Boyle skip the squat, but uses incline bench press. I can predict that in very near future incline will be ‘non functional’. Just my 2 cents.