Oh they do! They also have better pay restaurants, cushions on every pool lounger, and a lot of other tiny things I like better. But, it's an older crowd and not many kids and no play things like Rock Climbing or Flowriders. That's why Royal was the win for our family cruise.
I was Diamond before I sailed with Celebrity. When I booked my first one I called Celebrity loyalty program and boarded the ship as Elite. It works both ways. If one had only cruised Celebrity and booked a Royal they can call and get equivalent status on Royal. Which is very nice!