I have built many trailers over the past 36 years and most of what I built were tandem axle trailers. The last trailer I built was to use a pickup truck bed and put my 1969 Avion C-11 on it. It has a single 7,000# Flexiride axle under it and I just got back from an approximately 5,000 mile trip. I towed it over the mountains at Silverton and close to the Canadian border in Montana. It didn't sway or create any problems and that includes heavy cross winds and passing semis at freeway speeds along narrow roads.
There are pros and cons to both. The redundancy of a tandem axle is nice, but if you use a rubber torsion tandem axle, you don't have the equalizer which is very nice to reduce the strain on the axles. In fact, many rubber torsion axle manufacturers recommend that you use a 1.25 weight ratio when selecting your rubber torsion tandem axles. Keep in mind, over a large bump one of the rubber torsion axles will take most of the load. Having said that, rubber torsion axles give a better ride, and that is why I selected one for my single axle trailer. I also set it up to use the same tires and rims as my F-350 so I now have two spares. The way your trailer will tow has more to do with how well it is made and the quality of axles used than it does which axle arraingement you select.
My single axle trailer towed exceptionally well for about 5,000 miles with no WDH and I had about 6,000# on it, including the trailer weight.