Re: B Science (Financial Mathematics and Statistics) vs B Commerce/Science (Finance/M
Financial Mathematics and Statistics is a Science major and incorporates study in both Mathematics and Statistics, you can take electives from this major in most courses at USYD. Finance is a Commerce major and is only offered through Business School courses, thus you can't take any Finance electives if you aren't studying a Bachelor of Commerce or one of it's various combined degrees or Commerce (Liberal Studies).
In terms of the content, Finance is heavily grounded in mathematical theory but is, in my experience, more reliant on statistics than maths. There is also a strong focus on applying statistical concepts to come to a conclusion about something. Financial maths and stats requires study of both statistics and mathematics and as the subjects are offered through the Department of maths and stats in Science (not the Business School), they're much more theoretical than the applied focus of the Business School Finance major.
In terms of employment, it's much the same to my knowledge, although you have to consider whether your marks will be better coming from Finance or Financial Maths and Stats. Both are extremely hard to do very well in. Finance subjects, especially in 1st year, have high failure rates. In Maths and Stats, there are regular and advanced streams and it's very difficult to get a Distinction or above if you are in the regular stream. A criticism I've also heard of 2nd and 3rd year Maths/Stats at USYD is that it's too theoretical and has no practical application outside academia.
Another option you may want to consider, if maths and stats is your thing, is the Quantitative Business Analysis major from the Business School. It can focus on Operations Management or Statistical Modelling and is a very broad major that prepares you to work with quantitative data within and outside of the Financial Services sector.