Yes, mainly stability and less fishtailing with a double wheeled trailer. However, this can be mitigated somewhat towing a shorter wheelbase trailer like with the Extrawheel. The BOB trailer is a somewhat dated design these days, but it is very popular with mountain bikers and road riders alike due to its availability, decent resale value (seemed like everyone's looking for that trailer always) and parts supply.

To keep a single wheeled trailer stable, pack less and keep weight as low as you can and you should be fine.