It depends on your family, how you tour and the kind of stamina your kids have. For example - a character breakfast in the parks before opening might be a good idea, especially if you're done eating before opening. No park time wasted an some character time for the kids. When my daughter was 17 months, she was normally a late sleeper, so we would pry her out of bed *much* earlier than usual, hit the parks for the opening hour or two and then take a break for a late breakfast so she could recharge. It gave her the energy to happily do more instead of being miserable.
My neice doesn't eat well on the go, she has to sit and take her time. So a sitting breakfast (CS or TS) is the only way to get her to eat enough that she isn't cranky-hungry all morning. On vacation, I like to take it slow some days. Sleep in, a liesurely breakfast that's something I wouldn't make at home, meander around and take in the sights..
If you're ride people, and want to do all rides, al the time, then a TS breakfast might not make much sense for your family. What you're paying for at 'Ohana's breakfast is the characters btw - Kona is character-free.