Historically Ansett has always been the better of the two. I certainly prefer them. In the old days of Qantas flying exclusively international routes and TAA flying exclusively domestic routes, both were state-owned. And while this stupid arrangement was never going to make money, the go't made things worse by allowing the mngt of QF to choose it's own domestic partner. In any other country the two state-owned airlines would be tailored to fit each other, but QF chose Ansett, the privately-owned domestic "competition". Bizarre I know, but it shows who had the best service. Now TAA and Qantas are one airline, but the smell of nationalised industry still hangs heavily. Ansett have always had to make a profit.
That said, the Aussie airline industry is a classic duopoly and effectively there is no competition. I doubt there is any difference, although I haven't flown Qantas domestic routes (always Ansett). If I had $100m I'd buy some uprated A321s and some A330s and show them how things are done, and what competition really means.
fly Saha Air 707s daily from Tehran's downtown Mehrabad to Mashhad, Kish Island and Ahwaz