On Royal Caribbean, the rate for 3rd and 4th passengers are the same regardless of age. It is one rate for passengers 1 and 2 and a discounted rate for additional passengers.
This is NOT the case on Disney. While they have one rate for the 1st/2nd passengers, the rate for additional passengers is age dependent and children less than 3 are heavily discounted (even when compared to a child that is a 3rd passenger.
For example, I just pulled up a random cruise on Disney's site:
Guest 1: $1757
Guest 2: $1757
Guest 3: $945 (age 5)
Guest 4: $577 (age 1)
So No, Royal Caribbean does not discount for babies, but Disney does. Royal Caribbean's policy is more of the norm for the industry. This makes Disney a great value for families with kids less than 3.