The difference is that there isn't even fake judicial review. And I disagree that we have a stronger set of rights -- the difference is that the NSA explicitly ignores your constitutional rights.

All of our rights (other than the right to a jury for certain criminal trials, freedom of religion, the aquisition of property must be 'on just terms', the right to be a senator if you can vote, and the right to vote in federal elections) are in common law. This means that any new law can overturn those interpretations.

Personally I think Australia needs to push for a constitutional bill of rights. Unfortunately this is going to be a very hard battle to win, given the enormous requirements to get a constitutional amendment passed.