Fitting an updated rear anti roll bar will definitely reduce understeer. On its own, it may mean the rear has a tendency to oversteer on wet and greasy roads. The issue with too much oversteer is it reduces steering wheel feedback and may not alert the driver of breakaway before it happens. It may result in a car which is nervous in the wet which cannot exploit its possible increased cornering power. Add into that that people tend to fit new tyres to the front which results in age-hardened rubber on the rear which doesn't grip in cold, damp or wet and it may be simply a good way to pirouette down the road. It would probably be superb in the dry.
John's 20mm bar is likely ok for him in oz. I'm sure John has good experience of RWD and is skilled at drifting cars. I cannot say for sure but I'd advise caution in considering an uprated rear ARB. I think that should be about the last thing on the list.
For mine, the massively stiffer rear ARB was a huge improvement effected with stock springs and dampers. The car is very drivable, and I find it still fairly forgiving in slippery conditions (I've certainly had no scary moments on a slippery road since fitting it, thoug I'm somewhat circumspect on wet roads...).
If we wish to limit body roll, and improve steering and handling response, then stiffening something up will help (a little to a lot, depending). That something could be the springs, or the ARB, or the damper rates (though stiffer dampers don't limit the ultimate degree of body roll in absolute terms, they do slow the rate of body roll down and speed up the rate of weight transfer, so the elastic roll limit created by the combined spring and ARB rates may never or rarely be reached, depending, so body roll tends to feel
significantly reduced with stiffer dampers).
A stiffer ARB is relatively easy (and relatively cheap...) to implement, has relatively little affect on ride stiffness (compared to a roll stiffness equivalent increase in spring stiffness), and doesn't really require a stiffer damper to control it. So, IMO increasing ARB stiffness is very often one of the first things on the list, certainly so if not fitting stiffer springs (which would then most probably require stiffer dampers too).
Some related speculation:
In slippery conditions (especially heavy rain with standing water on the road) it may well be beneficial to reduce the amount of 'rubber on the road' at either axle line, which can be achieved with narrower tyres or effectively achieved with increased weight transfer (at an axle line). Increasing rear roll stiffness will increase rear weight transfer, i.e. for a given degree of lateral force more weight will transfer from the inside rear wheel to the outside rear wheel. Since weight transfer per degree of lateral force increases with increased roll stiffness (i.e. stiffer ARB and / or springs), more weight will transfer at a lesser lateral force, so, it might be argued that increasing rear roll stiffness (ARB and / or spring stiffness) might actually improve rear grip in slippery conditions.
What I mean is that (with greater rear roll stiffness) the inside rear wheel will unload more at lesser lateral force, so the outside rear wheel will become more heavily loaded earlier in the corner, and its' grip may therefore be increased. So, rear grip may actually be enhanced on a slippery surface.
However, increasing rear roll stiffness (whether by increasing ARB stiffness or spring stiffness) also makes the outside suspension corner stiffer in bump / rebound when the suspension is also in a 'rolled' state. If the outside wheel then hits a bump it may not be able to follow the road surface as well, so could momentarily lose 'weight' and so lose grip on the slippery surface when a rougher surface is encountered.
Once a tyre has lost grip and started to slide it is significantly harder to regain that grip than it was to lose it, which is why when a tyre locks up when braking too hard the driver needs to lift off the brake pedal quite a lot before grip is regained (pre ABS days). This can be a stronger affect on a slippery surface. So, on a slippery but smooth surface it may be beneficial for rear grip to increase rear roll stiffness, but on a less than smooth surface not so much. Perhaps it is this which can make a stiff set up 'skittish' near the limit on a slippery surface, i.e. the suspension may have more grip on the slippery surface, but is more prone to more readily losing that grip if the surface is less than smooth? And on a slippery surface, once grip is lost it is more difficult to regain.