do different models have different aircon compressors?

Did you have your system checked before regassing? If you didn't you probably should of just incase it's leaking somewhere
I'm not sure if the compressor makes a difference to how cold things are. I believe the Berlina would have climate control which might be a better system.
Has you relative have the same year-ish car as you? like a VR/VS berlina? (Im guessing you have a VR/VS because you posted in this section) . Newer cars would have better air con because they are newer, but if you keep your parts upto date and no leaking.. it should be good

 

The air conditioning compressors are the same whether that car is a Executive, Berlina, Calais, Statesman, Caprice, Sedan, Wagon, Ute. But they are different on different models, VS, VT, VZ, etc, and different engines, V6 and V8.

 

How cool the air will get also depends on the colour of the car with white being coolest and black hottest. Also you must run the air on recirc and not fresh to achiever maximum cooling. Check that the copper pipes under the drivers side of the dash which go into the heater/aircon unit are cold with the aircon on....if hot, the heater is still on despite you dialling cold.
You can also insert a thermometer into the air outlet in the middle of the dash and the temp should be between 3 and 9 deg with air on recirc and med speed...do this after driving for about 15 mins or when you think the air is at it's coldest.
Finally, a ute should be icy cold so my money is on the heater still being on.(this is a common problem as control rod slips off vacuum switch)

 

The knob which gets hit by the white arm is not a knob - it is the switch and the the white arm depresses it which supplies vacuum to the heater tap which turns the heater off. It takes a bit of force for the white arm to depress the 'knob', which is why they bugger up.