Yes there is a significant price difference and the main decision is whether you want/need the children amenities....
Other cruise lines are adult focussed have few children programs, a tiny arcades. The kids don't have a chance to interact with one another.
Disney cruises don't have casinos and replaced those areas with "kid's only zones". On their cruises kids are allowed to run around the ship and mis-behave a little. For younger kids, there's flounder's nursery. Yes there's adult only zones like Quiet Cove and Palo's.
Pictures.... if you don't pay for photo's on other cruises.... you kids will want photo's with all their hero's throughout the trip. Disney characters also show up on some excursions.
Entertainment.... lots of first run movies. Spiderman and Guardians of the Galaxy are running now on many voyages.
Internet/wifi.... I don't use the slow time based wifi on other cruises. 24Mbps downloads with 1gb is great for me on the Wonder.
If you are focussing on price... how much do you love your children? At the end of the day, the kid's will be much happier, but you will be paying significantly more for their happiness.