Costs also depend on the ship you book, where the cruise goes, how long the sailing is, the ages of the guests in your stateroom, the cabin location and more. To get the best idea of cost variances between Carnival and Disney,

"These ships clearly represent the next generation of Fun ships," according to the company. "They will be experiences unto themselves."

Carnival’s Conquest class ship could accommodate 1,000 more passengers than the current ship operating out of Baltimore’s port, the cruise line said.