Well, technically, those "hordes of unskilled labourers" aren't being granted citizenship. But generally, from my vantage, it's been a lot easier to immigrate into Australia than in the US. Some of my uncles and aunts were only able to obtain US citizenship because they'd served in its military. But my Australian relatives were able to obtain citizenship right off the bat just by applying for it (though admittedly, I'm not sure if it's still that easy today).
As for economic structure, Australia is far more to the left than America. Over at uni, a lot of us are appalled at how far to the right even Democrats in the US are. Here, we have high minimum wage, universal health care, generous unemployment benefits, and a whole lot more. And what has it produced? A far more egalitarian society, and one of the highest living standards in the world. In terms of HDI, for instance, Australia ranks #2 in the world (just below Norway, another socialist country).