We just recently cruised on the Voyager just to see how it compared to Disney.
First the Voyager is a great ship! Some things you won't find on
DCL include - rock climbing, mini golf and ice skating. The shopping is not that much better even though
RCCL has a huge "mall" like area in the middle of the ship.
Staterooms - On RCCL we booked a junior suite (like a cat 4 on DCL but even larger and nicer). The price was very good too! RCCL wins hands down on the stateroom - walk in closet, full tub, huge balcony with two chairs, a table and lounge chair too.
Food - It's not even close in my opinion - dining on DCL is far better than RCCL. The dining rotation is what makes DCL so much better - let's face it, its boring to eat at the same table ever night, and the food - RCCL quality is below average.
Entertainment - Even in my opinion. Both have great shows. RCL's guest performers (we had the Platters) are something unique. I don't care for casinos so I think DCL has the right idea - give that space to the kids clubs.
Kids - DCL wins here. On RCCL the clubs close twice a day for lunch and dinner. After 10pm on RCCL you have to pay extra for childcare. Don't get me wrong, our kids like RCCL but from the parents perspective RCCL is a hassle with all of the checking in and out. However RCCL is trying to catch up. In fact the kids club director (Nohair Pierre) was hired away from the DCL Magic where we knew him.
SPA - Since the Voyager has more spa their spa is more elaborate however they do not have a thermal suite (Rainforest). Spa treatments are more expensive on RCCL for the same thing. Overall Spa service is about the same.
Price - RCCL initial price is a bit cheaper than Disney and we got the best deal on RCCL at Costco. Once you are on board Disney may be a little less expensive for incidentals, alcohol, etc.
RCCL Voyager is a mega ship after all and in my opinion this made me feel my cruise experience was not as personalized as it was on DCL. You definitely feel part of a huge crowd.
So, in the end, we are still partial to Disney. It's just a more magical experience.