Both Trevermonty and Gary in the last two posts make relevant points.
As I think most of us know already, each time you change a caravan regardless of the number of axles, or it's size, it feels different to tow, and it takes some time to get used to the combinations nature. The differences may not always be huge.
Even if you don't change the caravan, just loading differently or fitting dampers can produce a change in the way it feels to tow.
In addition to using caravans for holidays, because of the work I did, I have towed many different mainly new caravans behind a wide range of different tow cars and vans, and from that experience I can say I prefer to tow longer caravans whether single or double axle.
The main difference I detected between SA & TA was how TA's would double tug the tow vehicle when each trailer wheel traversed a road imperfection or level crossing, and how they were less inclind to pitch so much under breaking. I can understand how such sensations may give a sense of stability.
I can also understand how the thought of having two axles can seem to offer a belief it must be better, and yes there can be an advantage if one tyre looses pressure the fact there's another on the same side is probably a good thing.
But overall I have not seen or experienced any evidence that having a twin axle endows better stability to car and caravan outfit.