I've done it with snow shoes, with skis and with neither. The snow shoes were quite useful for some areas when we were lucky enough to have some very deep snow. But the snow in Tassie is sometimes not great for snow shoes, when it is soft underneath with a thin hard icy crust on top. The snow shoes can fall through the crust into the soft stuff and be difficult to pull out again. It doesn't happen often, but if the conditions are wrong it can often enough to drive you crazy.
I was grateful for the snow shoes for some stretches, but sometimes just waded through the snow without them.
They were invaluable where the snow was well over waist deep for long distances (and over head high for short stretches). But I'm not sure if I'd bother taking them again.
I did a detailed trip report of our Snow Shoe trip in the topic at:
Overland Track Snow Walk, August 2010. I think I gave a description of how two different types of snow shoes worked for us in there somewhere.
(Cross country skis worked much better, but they are a serious pain in the bum to carry through forest - either too low and you hit them with your legs, or too high and you catch every branch you walk under. But it was worth it to ski down Mt Ossa! - a little way)