Ten reps on the rings aren't the same as ten reps on a dip station, especially if you're a big guy. The rings' instability engages much more of the core and eliminates the need to add load with a weight belt.
The Ring Dip
The main reason I like this exercise has to do with the law of irradiation – the contraction of the muscles surrounding a target muscle bolsters that exercise's strength and stability.
The rings' instability forces you to work much harder to stabilize the shoulder joint. That means the pecs, upper back, and traps get much more involved to "help" the triceps than traditional dips, which is a saving grace for bad shoulders.
With rings, you can customize just how internally or externally rotated you want your hands and arms to be. If you're a real rock star, try rotating the palms forward on each rep.