Yes, you get equal recognition in Celebrity's Captain's Club. When I made RCI Diamond I was immediately upgraded to Captain's Club Elite level. I already was a Captain's Club member so I don't know the process for C&A members who aren't CC members. I assume they just activate a membership for you once you book a Celebrity cruise.
I am quite fond of Celebrity. It is a more serene cruise than RCI offers. You need to look at one of the Solstice class ships.