Some minor items that I have experienced. May not be true on all ships. Anything can change at any time. e.g., Celebrity used to let PAX take on 2 wine bottles per person vs. Royal's 1 but that changed.
Almost forgot, it doesn't really bother me but irritates my wife, Celebrity provides hair conditioner in the shower, Royal does not. At least that is what I remember.
Also, I think Celebrity does twice a day room service (ie, turndown in the evening), Royal went to once a day.
Not sure if it was mentioned, I seem to remember that Royal allows smoking in the Casino and Celebrity does not.
I think Royal still has formal nights, Celebrity has Evening Chic. Not sure that there is a real difference other than the names.
Celebrity has Aqua Class and Royal does not.
Celebrity doesn't make you sign out pool towels, Royal does.
Royal sells a coffee punch card so you can prebuy specialty coffees at a discount (lots of discussion on the boards as to whether it is a true discount however for me it is).
Celebrity doesn't really limit the amount of non-alcoholic beverages you bring on, Royal does.
On the ships I have been on Celebrity usually has an outdoor grill near the pool that is free. Royal does not, Royal typically has a Johny Rockets that is extra charge.
Probably much more stuff that I don't remember.