Comparing Bristol's prices to Sydney's:
Rent: Sydney is maybe 50% more expensive. There is no council tax in Sydney, and the houses are bigger.
Food: In Sydney, groceries are usually more expensive (prices seem to be seasonal), but eating out is cheaper. The overall variety of food is better in Sydney, but Indian food is better in Bristol.
Booze: Beer is maybe 30% more expensive in Sydney, there is much less variety, and the pubs are less cozy. Wine is much cheaper and better in Sydney.
Bills: gas and electricity bills are both much, much cheaper in Sydney.
Transport: I don't own a car. Public transport is better and cheaper in Sydney than Bristol.
Food is a lot more expensive - but I guess if you eat cheaply or take advantage of office perks it could get the cost down.
Alcohol / going out is a lot more expensive.
Fuel / public transport is cheaper (but public transport is not as good in Sydney).
Tax is slightly less with no National Insurance to pay, and the employer is not paying it an sticking that into your Superannuation (Pension) instead.
I more than doubled my salary moving from the UK (Bristol) to Australia (Sydney), while my living costs only went up a little higher.