If the degree you wish to study doesn't have any requirements besides a specific ATAR, and if you get an ATAR equal or superior to the ATAR required by the degree, you will definitely be able to get into UNSW or USyd.
If there are no specific requirements in terms of completing a particular subject, as with UNSW's lack of prerequisites and emphasis on assumed knowledge, then the subjects you take in high school won't matter in terms of getting accepted. The benefit of doing a subject that is related to the degree (and considered assumed knowledge like Mathematics Advanced for UNSW's Bachelor of Economics and Bachelor of Commerce) is that it will allow you to be familiar with content taught particularly during your first year. Examples include studying Economics and Mathematics Advanced, which will familiarise you with economic and mathematical concepts that are covered in your first year at UNSW.
USyd seems more strict in that regard, as completing Mathematics Standard does not meet the minimum requirements for either its Bachelor of Economics or Bachelor of Commerce. USyd specifically requires an equivalent of band 4 in Mathematics Advanced or band E3 in Mathematics Extension 1 or 2.
The University of Sydney is introducing mathematics prerequisites for some courses from 2019 to help students thrive in their business, economics, science, technology, engineering and mathematics related degrees and prepare them to tackle future career challenges.
www.sydney.edu.au
Based on this information, it looks like UNSW might be your top priority because the fact that Mathematics Advanced is considered assumed knowledge for both degrees doesn't stop you from being accepted provided you meet the degree's ATAR requirement (unlike USyd, which requires you to meet its prerequisite in addition to the required ATAR), unless you decide to take Mathematics Advanced instead of Mathematics Standard, giving you the ability to choose between UNSW and USyd.
I hope this helps!
