I don’t think Boxer will be bought for Phase III. The only way I see that happening is if a tracked vehicle is simply unaffordable. Clearly, my bet is either Lynx or Puma. Each vehicle will come with the Lance turret and a number of common subsystems, which will make training and support for the whole fleet so, so much easier and cheaper. It would be possible for Australia to provide the Lance turret as government furnished equipment to put on some other contender, but the problems with that are obvious.
Between Puma and Lynx, I think it will come down to a mixture of cost and carrying capacity. With the move (back) to dedicated mechanised battalions, each section will only have six dismounts, which means a section will fit in Puma, which is almost certainly a more capable vehicle than Lynx. However, army may still decide that a vehicle that can carry eight dismounts is still needed/preferred (for when we inevitably change our mind again about section size etc), which would make Lynx the more attractive vehicle as it is the only one that can fit eight dismounts.
Puma will almost certainly be more expensive than Lynx, so if the budget is particularly stressed then that might be a more attractive option. I don’t think the not-off-the-shelf nature of the Lynx will be as big an issue as some state, as pretty much all the subsystems are proven, Rheinmetall are hardly new at this, and there is a lot more appetite for developmental risk for Phase 3 compared to a Phase 2 (although still not much).
Of note as well, is that it is very unlikely we will buy a full 450 vehicles. That was planned off eight man sections, 40 man platoons and eight vehicles to lift a platoon. With the change in orbat, only four vehicles are needed to lift the platoon. I think only about 75% as many vehicles will be needed. The obvious so what is that the budget won’t be as stressed, and a more expensive vehicle becomes more of an option.
My tip in descending order of likeliness is:
Puma/Lynx
Boxer
Other vehicle with Lance turret
Any other vehicle