One couple we encountered on the Rhine Cycle Route had a little girl of about 18 months with them. They used both a seat and a trailer. He pulled the trailer, and the little girl (and dog) slept in it sometimes. She had a handlebar seat on her bicycle, and the little girl sat in it some of the time.

I thought the variety was a good idea ... each parent dealt with the extra weight of the child some of the time, and the child was able to either sit and look around at everything some of the time, and sleep some of the time.