DH and i are lucky - even though we're pretty young and still work full-time, our jobs are flexible and so we have the opportunity to travel a lot. we both also prefer "experiences" to "stuff", so if we have extra $$$ we tend to spend it on trips.
disney and royal are probably more alike than different. i should say up front that royal is my favorite cruise line, so i'm a little skewed in their favor, though we enjoy disney enough to cruise them pretty much every year. the big issue for me is that i'm a night person, and disney is pretty dead at night, while royal has tons going on until midnight or later. i don't drink and don't really gamble (maybe a slot machine here and there, but often not even that) and i still find plenty to do on royal in the evenings. i should also mention that i've been on a number of royal ships, but they've all been the newer/bigger ones, so an older or smaller royal ship may be a different experience than what i've had.
so, in general terms:
i think disney's rooms are better - they are bigger and have the split bath. that said, for the price of a disney room, you can often get a suite on royal, which will be larger with a larger balcony, and sometimes a second bathroom depending on the room type, as well as suite perks (concierge etc).
overall disney's service is usually better. on royal, we've almost always had stellar room stewards and dining room servers, but some of the other staff (guest services, photo shop, etc) are sometimes meh, and occasionally even rude. on disney, our room stewards have been great, and staff elsewhere are almost always wonderful. our dining room servers on disney, however, have also been kind of meh.
i think royal's ships/activities are better. we go on the newer ships with things like flowriders, rock walls, ice skating rinks, bumper cars, carousels, zip lines, etc. i am a ride chicken so i haven't done some of these (ok, most of these
), but it's fun to watch people do them, and i'm glad the opportunity is there. there's plenty to do even for us chickens - i've done the bumper cars, carousel, mini golf, cupcake decorating classes, parades, dance parties, behind the scenes tours, etc, as well as the usual swimming, movies, bingo, and similar. i'm signed up to try the skydiving simulator on my next royal cruise, and am trying to psych myself up to do the zip line on another cruise next fall. on disney, other than mini golf and the midship detective agency on the newer ships, i don't feel like there's as much to do. i also love the promenade on royal, which is a multi-story space down the center of the ship that has shops and restaurants - it's a hub to see people and where activities like the parades are held. i do love the look of disney's ships, especially from the outside with the black hull etc, but i think royal's are organized better and even the mega-ships usually don't feel crowded. most royal ships have dreamworks characters and 3d movies, if you like that stuff on disney.
i think royal's entertainment is better, at least on the newer ships. we've seen the usual disney shows - golden mickeys, villians tonight, disney dreams, etc - and they were cute, but i still think royal has the edge. each of their newer ships has a broadway-style show (mamma mia, cats, saturday night fever, etc) and a cirque-du-soleil style show, and oasis class has a diving/water show that's incredible. they also do ice skating shows on the rink which are fantastic, especially when you consider the ships are often moving quite a bit.
as for food, that's totally subjective, but i think disney's buffets tend to be better than royal's, but royal's main dining room food is better than disney's. palo is my favorite cruise specialty restaurant ever, though some of royal's are close. disney of course has the rotational dining which most royal ships don't have.
phew, that was a novel!
if you have particular questions, just let me know!