I agree with Kuki, as a matter of fact, we took my two boys when they were 7 and 5 on one of those "awful, decadent" Carnival Cruises - it was one of the best experiences of their lives!
I would advise against letting anyone scare you away from Carnival - no lines are completely trouble-free, and there is a lot of jealousy directed at #1. You may have at TA that would rather you book a more expensive line, more $$ for them.
But, bottom line, it's your money and your life, so go with what feels right to you.
I hope you'll have fun whichever way you choose.