Well, it's debatable how much of Australia's history was shaped by the convict system. Right from the first ships the military guard was of a comparable size, and as soon as commissions and sentences ended, people were getting land grants so that free settlers outnumbered convicts pretty quickly. I think there were even free colonists travelling to Sydney in the 1790s, and certainly by the 1800s. Of course in the early days the convict system was important to primitive accumulation, both in that there was some free (but notoriously inefficient) convict labour, free land grants, trade monopolies (officers commissioned private supply ships on their own account) and a dependent colonial state. The first capitalists were the military officers, but they were joined fairly quickly by freed convicts and settlers.
It was only two or three decades before the colonies were capitalist agricultural colonies with a substantial prison industry rather than a convict society, and it was pressure from the colonial population that ended transportation.
New Zealand was a few decades behind in getting off the ground. Pre-1840s there were only a few outposts of European settlement – a Wild West of the sea with whalers, a few traders and missionaries. The Wakefield colonies were much more important in NZ than in Australia – In NZ all the main centres except Auckland started as Wakefield colonies, in Aus I think only Adelaide. Of course, see Capital vol. 1 on Wakefield, since Marx was fascinated with his main idea, which was to attract working colonists and price land high enough to keep them as workers rather than landowners.
>From then NZ and Australia had fairly similar industrial histories for
quite a while: sheep wool being the main export industry until
refrigerated shipping in the 1890s opened up other possibilities; gold
rushes in the mid-19th century, railway building and so on. There was
a huge difference in the aboriginal populations. Australian aborigines
were scattered and nomadic hunter-gatherers with many separate
languages; Maori were a tribal but more or less unified (by language
and trade) semi-agricultural civilisation. So there was full-scale
warfare in NZ, especially in the Waikato where a hostile 'King
movement' united some tribes and maintained a forest stronghold for
years in the 1860s. After that the main military resistance came from
really interesting prophet-led rebellions.
In the first half of the 20th century I think development was fairly parallel – both countries were agriculture-centred, with some industrial development in the cities, centralised arbitration systems, currencies based on the British pound etc. It was only after WWII that Australian mineral development took off in a big way and really only since the 1960s that Australia started to take off from NZ, because the latter suffered from a more limited base of primary commodity exports with generally declining prices.
Like I said the major difference in class composition is ethnic. Both countries had White Australia/NZ policies but Australia's was stronger and lasted longer. Maori are a much bigger proportion of the population in NZ than Aborigines in Australia: 14.6% vs. 2.6%. That means Maori have never been able to be politically ignored in the way Aborigines are. Australia has a much larger Mediterranean make-up in its European population, based on post-war migration, including first Italians and Greeks and since the 1980s Lebanese. (Sydney has the biggest Lebanese population outside Lebanon I think.) Both countries have substantial Asian populations, mostly Chinese (10% in NZ, 7% in Australia). There is also more of a Pacific Island presence in NZ. Nowadays NZers living in Australia equal about 10% of the NZ population (including me) I guess mainly because wages are higher and the climate more pleasant.
The union movement is politically quite a bit stronger in Australia than in NZ for whatever reason, partly because anti-union legislation passed in NZ in the early 1990s. Australian politics has both an uglier right and a stronger left than NZ. Also, Australia has big metropolitan cities and NZ doesn't, which I think makes a huge cultural difference.
Cheers, Mike