Well, I'll be the first to jump in and say...not necessarily.
I've gotten good service on each line I've sailed and only one truly miserable experience...it was on Disney. Granted, it was outside the norm, but that can happen anywhere.
Food is better on other lines.
Kids clubs...depends on your kid. Some love
DCL, some prefer others, and some won't go in a kids club on any line. It varies by child.
While Castaway Cay is nice, I've been to three cruise line's private islands and Half Moon Cay is hands down the best. (Shared by HAL and CCL)
Disney shows are great but it really depends on the type of entertainment you prefer. I do like that their shows are early if you have late dinner seating. On other lines, I rarely see shows because my eyes start closing at 9 p.m.
The Carnival Breeze (which sails out of Miami, I believe) has split bathrooms in their Deluxe OV staterooms, too. While I love the split bathrooms, I will give them up in a heartbeat for the shower in the Aqua Class rooms on Celebrity.
Having a movie theater onboard is great on DCL, but it was pretty fun watching movies on deck on other lines, too.
Nickel and dimeing happens on all lines, including DCL. They just don't do it as much because as a general rule, their fares are much higher than other mainstream lines.
It really just depends on you and your family. Do I think it's worth the extra money? No. Do I think it's a great cruise? Sure! But I love to cruise and love them all. This is a Disney board, the answers you get are going to be skewed in favor of Disney. If you'd like to research other lines, go to the boards at Cruise Critic.
Whatever you decide, enjoy your cruise!