I have done
Royal Caribbean and Disney and honestly- unless I win the lottery I won't go on Disney again. My
RCCL cruise was $400 more than Disney- but 4 nights longer for a nearly identical cabin!!!

And the food was better on RCCL and their private beach (Labadee) is nearly as good as
Castaway Cay.
Just an FYI, some cruise lines the 2 year old won't be allowed to do any activities, some he will. This is where I recommend calling a
travel agent that specializes in cruises and going onto the Family Board at CruiseCritic.com. I *think* a 2 year old is allowed to do activities on Carnival (may have to be potty trained.) On RCCL it used to be a strict 3 year cut-off, but I think the newer ships are putting in somthing for the younger ones.
On RCCL I went on the Independence (same as Freedom and Liberty) and they have the H20 zone which is great for your boys. The Liberty tends to gave some really good deals, my parents are doing a 5-night in Dec that is very inexpensive.
A cruise professional can also help determine if you need passports or not. There are some cruises you do not need them, just an FYI if there is an emergency (miss the ship at a port, need to be flown back to US for medical reasons) not having a passport could be a problem. Passports have gotten very expensive and for the kids under 16 it is only good for 5 years, the 16 year old's it is good for 10.