We started out with a seat, and when Kidlet #2 came along, we switched to a trailer. I much preferred the stability of towing the trailer over the kid in the seat. As for errands, the trailer freed us up to run more errands, as there was room for a couple of bags of groceries, etc., in it. We also were able to take the kids on a couple of half century (50 mile) rides in the trailer as there was room for toys, books, food, kicking each other. :-) We couldn't have done that with the kid seats.
Safety? I haven't looked for any stats for a long time. But, a kid in a seat has considerably farther to fall than one in a trailer. A lot of times it's the vertical distance that's far more dangerous than horizontal speed, especially for head and neck injuries. My sister managed to flip her kid in a trailer and he hung upside down quite secure, asking if they could do that again...