I think I'm right in saying that a nuclear powered submarine can maintain high speeds (typically around 30kt) for pretty much indefinite periods. And they only need to surface when they run out of provisions for the crew. Given Australia's geography, that's not an insignificant consideration.
AIP submarines move much more slowly when using AIP compared to diesel or nuclear submarines. I believe (but as ever, happy to be corrected) that's typically around 5-6 kt if the sub wants to remain submerged at maximum endurance, which is too slow for long-distance transits or traveling with surface ships. Because current AIP technology doesn’t produce enough power for higher speeds, most AIP submarines also come with back-up diesel engines.
Hence nuclear being the best (as well as the most expensive) option for Australia, given the distances involved in getting the boats where they might want them, and the speed at which they can get there - coupled with the fact that they can do all that quietly and without surfacing for months at a time. If that's a club that you want (or need) to be in, then you have to pay the entry fee...