Welcome to Cruise Reviews. Both cruise lines would be good for you and your family. They both will have activities for your children. I would look at both cruise lines and compare not only by price, but by the itineraries and length of time in each port. The NCL Spirit is doing a more exotic itinerary going to Roatan, Belize, Costa Maya, and Cozumel. The Carnival Conquest is doing a more traditional Western Caribbean going to Jamaica, Cozumel, and Grand Cayman. If this is your first cruise you may enjoy the traditional better especially with the children. Grand Cayman has the Swimming with the Stingrays which is very popular and Seven Mile Beach. In Jamaica, Dunn River Falls is the most popular with an opportunity to walk up the falls. Snorkeling is great in all three of the traditional Western Caribbean ports. Cozumel has many beaches to choose from. Many like Paradise Beach and there would be water toys for the children.
If you are driving to New Orleans then you may want to take your snorkel equipment. If you're flying then consider all the room they will take up and cost of checking luggage. The ships do offer snorkel tours which will include the equipment and also your transportation to and from the beaches. With a family of four it may add up to be pricey booking through the ship. However; keep in mind the cost of the transportation included and the security of booking through the cruise ship. If you take a taxi and go off on your own you must be aware of allowing enough time to get back to the ship. The ship will require you to be back 1/2 hour before it sails and they will not wait! When you book shore excursions through the ship they will hold the ship if the tour you're on is running late.