I'm majoring in maths, stats and economics at USYD.

Statistics is without a doubt far more useful to you. Mathematical statistics is highly rigorous, and bits and pieces of pure maths even leak into it (e.g. the measure-theoretic construction of probability). A lot of students dislike statistics, mostly because first-year statistics is often compulsory, not very rigorous, and often taught badly. Statistics will also involve a bit of computing, which is useful and can be interesting sometimes.

I haven't had much experience with pure maths yet, though by the time I graduate, most of my senior maths units would be pure as opposed to applied. Pure maths is very fascinating in and of itself, and it can help you read and understand maths in a completely different, rigorous perspective. The study of pure maths involves contemplating abstract objects and relations in isolation of physical contexts. Though pure maths should not be taken as a means to secure a job, but rather out of your own interest. The main career pure maths majors tend to go into is academia, though sometimes having training in pure maths may get you employed as an applied mathematician (however this isn't something you should rely on). Applied maths is obviously more useful for the financial sector (though likely not as useful as statistics...). If you're studying at USYD, then you can major in maths with your own personal mix of pure and applied units.

Good luck!