Dips on rings significantly increase stabilizer muscle activation. If you include a training phase with ring dips and then switch back to parallel-bar dips, don’t be surprised if your strength gets a noticeable boost.
That said, ring dips are highly advanced and not for everyone. Beginners should master ring push-ups before attempting dips to build the necessary stability and control.
Be aware: ring dips have been responsible for numerous chest and shoulder injuries in CrossFit. This is not an exercise to do at high speed or under high fatigue. Perform it early in your workout, brace tightly, and focus on slow, controlled reps.
For more tips, check out this post on ring dips.