I'm not a fan of the children's menu. My son has/had peanut allergies so the PBJs are out for him. They don't like pepperoni pizza (only gourmet chicken pizza for them!) and if DH has his way, they will NEVER taste a hot dog. There are only so many hamburgers/chicken fingers you want your kids to eat (although the chicken fingers on Carnival are VERY good).
When we sailed DREAM, my daughter had just turned 4 and my son was 2 1/2. For lunch, we alternated between burgers and chicken fingers. For dinners, we ordered off the adult menu for them, and they would generally split a chicken or beef entree. If your kids have grown-up tastes, don't be afraid to let them order what they want. We would read the menu to them and let them decide. Oh, and they started EVERY dinner with a shrimp cocktail, except for the night they wanted the sushi appetizers.