IMHO, there is one HUGE difference between the one and two wheeled trailers. All the other considerations are relatively small.

A one wheeled trailer, especially when loaded, will greatly affect the handling of the bike. Most especially while standing.

A two wheeled trailer won't. You can stand all day and rock from side to side and the bike will handle almost as if unloaded.

If you don't stand much when you ride, then a one wheeler is a good choice. If you stand quite a bit, a two wheeled trailer is better.