A new born baby can't support his head with his neck muscles. I don't remember when that goes away. Someone here will probably know. Some trailers will list a minimum age.
I think that the kid trailers are safer. Loading a kid into a seat on the bike requires balancing the bike at the same time, even on a kickstand. Also if you fall sideways the kids slams into the ground. Even if protected by the baby seat and a helmet it's a big hit.