We've sailed with Royal several times and have sailed on Explorer of the Seas (out of NJ to Bermuda). We did the Baltic Cruise on RCI last June and had a great time.
I will say that for families,
RCCL doesn't hold a candle to
DCL. It just doesn't....particularly for the European cruises. They didn't have enough kids to really have a robust kid's program and it the demographics of that particular cruise ended up being most senior citizens. We WERE NOT expecting this on a summer cruise on RCCL. What is meant was that the kid's were pretty much forgotten....there was nothing for them. At one point, my 12 year old went to guest services herself and asked if they could please plan something for the kids to do----They ended up giving her credits at the arcade (which she thought was great)---but no programming. That being said...she climbed the rock wall 50 times on the 12 night cruise (really...it was a ship record)---because there were very few other guests even trying it once.
But the food was fine, our service was great, the ship was clean, and we saw a lot in 12 days. One other thing to note was that European itineraries were staffed with (duh!) primarily European crews. I'm not sure why we didn't think about this ahead of time. This meant that there were a LOT of jokes and even entertainment (music, pop culture references, etc) that was aimed toward Europeans. It was sort of fun as a cultural experience---but sometimes it meant that things went over our heads (and boy did the American bacon disappear fast)---but the hot steamed milk for tea was divine! This was wall good--just not quite what we were expecting so we sort of had to adjust to the fact that it wasn't the same "cruising experience" as we were used to out of the U.S.
As for the Explorer of the Seas---- we had an ocean view for that one and, honestly, it wasn't any more exciting that the typical inside stateroom we usually choose. We didn't spend that much time in the room anyway. One thing I don't love about RCCL for families is that the bunks are directly over the main bed. This means we hit our heads every time we had to get up in the night, etc. DCL has the bunks in a separate area of the room. I liked EOS promenade area (like a little mall with an atrium) as it was a nice place to have a cup of coffee and read a book. The ice show was fun, but the ice skating was pretty limited and we only did it once to say we did it. The kids liked the mini-golf, rock climbing and inline skating.
The prices for RCCL are so much cheaper than Disney that it does make it worth it if you are on a port-heavy itinerary. But go in knowing what to expect.....and have fun!