G'Day Fella's,

Ripp, as the other blokes have suggested, both the .223 and the .22-250, are very good for this job.
These days, I use the .223 but for decades, I got by with very accurate Tikka (model LSA 55) factory rifles, in .222 Rem.
Out West in New South Wales (NSW) and Queensland (QLD), where the shooting distances can be longer (Wide open plains and Skitish/Nervous Skippy's), the .22-250 is popular apparently. I hear that shots out there, can regularly be in the 200 to 300 meter range.
Around here (Southern Tablelands and the Monaro of NSW), most shots are in the less than 100 to 200 meters distance.
Most of this shooting (and it is Shooting, Not Hunting), is done at night using a spotlight. and standing on the back of a vehicle, as you drive around the paddocks looking for "Customers". If they are not in range, we usually just drive closer .......... sometimes.

Generally, I would use a 50ish grain bullet, but have been known to use 40 grain bullets on Cattle Studs, where an over penetration, could cost the shooter $10,000.00!
These particular Cattle, (Murry Grey/Angus Cross), blend into the back ground EXCEEDINGLY WELL at night unfortunately, and you don't know they are there, until the look at you, and you see the reflection of their eye's, in the spotlight. Never shot one, so luckily, never had to pay the bill.

The main reason most people I know, use a .222 or .223, is pure economics, for both Ammo cost and Barrel wear. If you are undertaking this work, it doesn't take you many years to shoot out a barrel, even with appropriate care and cleaning.
I also know of Professional Roo Shooters (Pro's), that are using 6mm PPC and 6mm BR chambered rifles, for this same reason (extending barrel life), with the added benifit of less wind drift.
When I was doing this, we would normally try to deck 40 or 50 Skippy's a night (and 99.999% brain shots or as a mate of mine (JC) calls them, "Aussie Heart Shots"). Any lesser tally, would only be a half hearted effort, and a waste of time, fuel and effort.

With the changes in the regulations, in recent years, I know some Pro's around here, that are now using .17 HMR rimfire rifle's to get the job done. The convenience, of not having to spend a couple of hours reloading, prior to a nights shooting, is a help to these blokes.
Just grab a couple of boxes of "Crackers", and head out the door.
Obviously the .17 HMR statergy, probably wouldn't work at the longer distance, out West!

Hope that helps

No Probs NitroX.

D'oh!
Homer