Australian English is much, much closer to British English.
With the exception of a few specifically Australian phrases, the English spoken by most Australians and New Zealanders is basically British English. Grammar, spelling, vocabulary...it's nearly all British.
The same goes for the accent. Australian and NZ accents are pretty close to the accents of southern England. In fact, when Aussies and Kiwis travel abroad, many people presume that they must be British. Even many Americans and Canadians would struggle to distinguish between a London accent and a Melbourne one. Just listen to Cate Blanchett!