We have the Burley Bee trailer. I wouldn't want to use a trailer on roads with traffic but we just take it out on a bike path. I think when you don't have to worry about cars the trailer is safer bc it is surrounded by an aluminum frame and if the bike tips the trailer doesn't.
My daughter really enjoys the trailer. She an bring toys and a drink in it with her and if its cooler we can use the cover and give her a blanket to stay warm. If she was in a seat we wouldn't have these options and I'm not sure she'd enjoy it as much. She has even fallen asleep in it several times so it must be comfy!
The two main drawbacks I can think of for a trailer are that it does make pedaling significantly harder. DD is 30 pounds and while our trailer can hold one or two I really can't picture pulling double her weight. Also, it takes a longer time to brake/slow down so if you bike on hills a seat may be better for those reasons.