We've done 3 Carnival cruises (Inspiration 2004, Imagination 2005, Liberty 2006) then our 1st
DCL earlier this month. We always take our kids and my parents love to cruise so they come too. Hands down, we all agreed the service on DCL is better. Of course you pay more so you just have to try it to see if it's worth it to you. I liked the little things like hand wipes outside each dining room, kid-friendly trays, fireworks, lots of family entertainment, Dis. characters.
We tried the Liberty after realizing the 1st 2 cruises were on older ships. Liberty was 6 mos. old when we sailed it. It was almost too big. Remember, no matter how many decks a ship has, there can only be 1 pool deck. The chairs on the Liberty covered almost every sq. inch of the deck and still was really hard to find a chair and we're early risers. You could barely walk just so crowded. (much more packed-in than the older, smaller ships) We did love the huge slide on the Liberty. We're not super active on our cruises and spend a large part of our day swimming/lounging by the pool. Liberty also has the big screen above the pool and showed Shrek and Finding Nemo. My boys 6 & 10 thought the Mickey slide/pool was for "babies." One nice touch on Carnival: the doors to the buffet area on the pool decks all have decorative glass doors that slide open automatically when you approach. It just skeeved me to touch the door pulls to go to Topsider's. You would think DCL would have thought of this considering there are so many strollers too. Sure would help parents trying to juggle food trays and children.
While Carnival has a kid's club, my kids weren't too fond of it and it's much smaller than DCL, but don't judge by my kid's taste cuz they didn't want to go to DCL club either.(1 day for 2 hrs, that's it!

)
Liberty's arcade was about quadruple DCL's: 4 air hockey tables and lots more games, even the kind you sit on and moves you around like virtual roller coaster thing. (hard to explain but it was neat) Carnival had a huge chess board on the pool deck-each piece is like 2-3 ft. tall. Looked like fun but we never did it so I didn't miss it on DCL.
Staterooms were similar in size (we had oceanview on all 4) Liberty's are 220 sq. ft. DCL's are 214, older Carnival's are 185. More & larger drawers on the Liberty. Same safe. The split bath on DCL made family living a lot easier. My boys could both brush teeth w/o fighting over sink, etc. I like the big curtain DCL offers that separates the "living room" from the "bedroom." Being the only female in the cabin with 3 males, I could shut the curtain and get dressed while kids watched tv. (on Carnival dh would take them to the arcade while I showered/dressed or I'd do both in the hot, steamy bathroom-way too hot!)
Stateroom host/hostess service was equal but no towel animal on last night with Carnival.
Room service is available on Carnival on day of debarkation which was a huge let down for me on DCL.
Dining room service was equal but more fun on DCL with rotational dining and Pirate night. Much noisier on DCL since there's so many more kids. Didn't bother me but I guess it would bother some people. Overall, food was way better on Carnival, somewhat bland on DCL esp. the steak. Loved those Mickey bars on DCL!
After dinner entertainment on Liberty is mostly adult oriented, not necessarily rated R but boring for kids. There are
some shows a kid could go to but here's where DCL won my heart: every night we had great family entertainment. Good wholesome stuff like magic shows, jugglers, singing comedians, and Broadway-like shows. Then later had an adults-only comedian which was hilarious too.
While I liked the photo packages available at Shutters, I like that on Carnival if you buy the original, you can get a reprint done any size you want, whereas on DCL if it comes in 8x10 all reprints must still be 8x10, which is basically a 6x8 with a fun border.
This part may sound corny but the crowd on DCL seemed much nicer and more polite. While I never saw the "party animals and drunks" that people think of when they think of Carnival, there would occasionally be some loud idiot that was mildly annoying. On the other hand, some people would find lots of whining/crying babies, toddlers, strollers and kids on DCL annoying. My bro & SIL (who have 1 grown child) came with us on the Liberty and declined DCL in search of a "quieter" atmosphere. I guess it depends on what is annoying to you.
Overall, if I had to vote for 1 or the other, I'd definitely pick DCL. True, it does cost a lot more but we had such a blast I just can't wait to do it again. I'd rather do DCL once every 2 years than Carnival every year.
JMHO!

sorry this is sooo long!