The main difference between a carbon tax (emissions tax) and an emissions trading scheme is this. With a carbon tax, the price of emitting a unit of greenhouse gases is fixed but the total level of emissions is unknown. With an emissions trading scheme, the level of emissions is fixed (capped) but the price is unknown.
It follows that choosing one over the other is partly an issue of whether you want certainty in your environmental outcome or certainty in the cost to industry.
The experience of the European emissions trading scheme and now it seems the US Regional Greenhouse Gas Initiative (RGGI, pronounce it 'Reggie' - a trading scheme involving 10 States in north-east USA) has been that the cap on emissions was set too high and too many permits made available, with high volatility in permit prices and permit prices crashing after a while. The governments were too worried about the potential cost to indsutry (which isn't known in a trading scheme, but has to be forecast) and so overallocated permits.
Australia's ETS will actually start out as effectively a carbon tax, because the price of permits will be fixed at $10 a tonne for at least the first year. After that it become a trading scheme, with a fixed emissions cap and an unknown permit price.
Actually, it's more like hybrid scheme in one way, because it's proposed that there will be a ceiling price of $40 a tonne: companies can buy unlimited permits from the government at that price, so the permit price will never rise above $40.
A lesson from the EU and RGGI is that it would make sense to set a floor price too, so everyone knows that the permit price will never fall below, for example, $15 a tonne. That gives some certainty to industry, that investments in emissions-reducing technologies that are profitable at a carbon price of $10 a tonne or more can be made with no carbon price risk. It gives some reassurance to renewable energy and similar industries that they can safely invest. And it means that if reducing emissions turns out to be cheaper than expected, some of the benefit goes to the environment in the form of lower emissions and doesn't all go to indsutry in the form of cheaper permits.