Both MasterCard and Visa are widely accepted in Australia and New Zealand. I would focus around the features of the card and the best deal for you.

Clearly, the best option will be one that offers you no foreign exchange fees. Both Post Office and Nationwide offer such products and you can find them within the Travel Money section of the Money pages on this site. The Post Office charges you less should you need to withdraw cash at an ATM.

http://www.moneysupermarket.com/travel-money/