Putting everything into your offset is going to be better - lower interest while the money is in there.
Paying by credit card, (and paying off the credit card completely on the due date), again, leaves money in your offset account longer, reducing your interest.
BUT .... it really depends on what your financial situation is, and how good you are with your money.
A lot of people struggle with the credit card option. Using cash, you have cash in your hand, and can see what you are spending. Credit card, not so much, so people are more inclined to overspend.
Same with the bills really - shifting money to another account regularly, yes, you loose the benefit of having it in your offset account, but having it there in the offset makes it easier to spend, and it can be easy to blow the budget and not have enough left to cover the bills when they come in.
Personally, we put everything in the offset. Bills come out of there. Most purchases are on credit card, paid off in full every month. But our spending habits are pretty good, and the system works for us.