Yes, the cargo bike is much better for transporting children, for the simple reason that the children are suspended on the same wheels as the rider. Kid trailers have two wheels, typically of smaller diameter than normal bicycle wheels. That's a double-whammy, because the trailer wheels don't follow the same track (they hit potholes the rider doesn't feel), and the impacts are harder due to reduced wheel diameter. Trailer suspension does not solve these problems. Aside from child hauling, trailers are harder to manage, assuming the load can instead be put directly on the bike.

I put over 7,000 miles on a Surly Big Dummy, much of it hauling my son from age <1 to 7. It was far safer and more comfortable for him than a trailer would have been. I've also ridden thousands of miles with a B.O.B. cargo trailer and a Tout Terrain trailer, and I would always choose the cargo bike if at all suitable to the conditions. The only thing I prefer the trailer for is hauling gear for trail maintenance.