Swags (as far as I know) are pretty unique to Australia. Started with Cattle drovers back in the 1800s and the 1900s. Even today to a lesser extent used by drovers. Those days it was more like an oversized canvas sleeping bag. The canvas kept them dry from water and the coldd conditions of the outback.
Today many overlanders still like the swag but designs have evolved, more aimed at the recreation market. The main difference to a dome tent, swags are made from canvas, comes with a mattress and accommodates no more than two adults. Some designs can take two adults and two children. Unlike in some dome tents, it is not possible to stand up in a swag.
I guess the main attraction for swags over tents is it's canvas construction (works well in cold desert conditions) and it also in part a sense of Aussie outback tradition.
RE: A New Swag To Keep My Wife Happy