Hi, Thanks for writing to us
MBA and MPA are both very good and profound masters. One is aimed purely on your accounting skills and the other on your overall business skills.
If you are a registered CA and have registration towards a body that is recognised by CAANZ, then you can apply for registration directly and be part of it. In this scenario even an MBA would be good for you as it would polish your business skills and you could always take a major in accounting.
If you would like to apply for registration to CAANZ and you are not registered with a professional body that has a MOU with CAANZ then doing a MPA course would be your best bet.