You will enjoy the Oasis. We are huge Disney fans and had only gone on DCL cruises before, but last year decided to try the Liberty of the Seas(not even as nice as Oasis). We were kind of nervous but we went in with open minds and had a blast. We all had mixed feelings, but my kids(teens) all liked it better due to all the activities, like the FLoRider, Ice Skating, rock climbing wall etc.
That said, here are some of my top pros and cons I noticed, at least IMO:
DCL:
Pros:
Better food, much nicer, personal, accommodating wait staff
That special Disney "magic", that "je ne sais quoi" that Disney has
Much more family/kid friendly
Entertainment- hands down WAY better all around, not just shows but the live music, bingo, etc.
Pirate night(and other theme nights if you get one of those)
Pin trading if you/kids are into that
MUCH better photographers and photo nights/options
MUCH better spa/massage
Cons:
Price
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RCCL:
Pros:
Very nice modern impressive ships
Much more activities. Ours had FLoRider, Ice Skating, rock climbing wall, cupcake bakery the kids did a baking class, Ice cream shop, etc.
Johnny Rockets for a casual eating option
Concierge service was very nice if you have a suite
Shopping "mall" if you like that aspect
Cons:
The staff did not seem happy to be there, a few even seemed disgruntled.
Seem to nickel and dime you to death for every little thing
The food services are not set up well for the pool area, especially if you have kids
Entertainment was lacking
The photos were poor quality, seemed like they just handed whoever a camera and told them to take pictures those nights.
Seemed like the masseuses were just whatever random staff didn't have anything to do that day.