The differences are mainly in the nature of the core subjects you must do. A finance major is the same regardless of the actual course you're doing (if that makes sense) because you are still required to do the same compulsory subjects.
The real differences are seen here.
Commerce cores
ACCT1501 Accounting & Financial Mgt 1A (6 UOC)
ECON1101 Microeconomics 1 (6 UOC)
ECON1203 Business & Economic Statistics (6 UOC)
MGMT1001 Managing Organisations&People (6 UOC)
Flexible core courses account for 24 UOC (4 courses). Students should choose four courses from the following list:
ACCT1511 Accounting & Financial Mgt 1B (6 UOC)
ECON1102 Macroeconomics 1 (6 UOC)
FINS1613 Business Finance (6 UOC)
INFS1602 Info Systems in Business (6 UOC)
MARK1012 Marketing Fundamentals (6 UOC)
TABL1710 Business and the Law (6 UOC)
Economics cores
ACCT1501 Accounting & Financial Mgt 1A (6 UOC)
ECON1101 Microeconomics 1 (6 UOC)
ECON1102 Macroeconomics 1 (6 UOC)
ECON1202 Quantitative Analysis (6 UOC)
ECON1203 Business & Economic Statistics (6 UOC)
ECON1401 Economic Analysis (6 UOC)
ECON2101 Microeconomics 2 (6 UOC)
ECON2206 Introductory Econometrics (6 UOC)
This is for unsw specifically but most unis will have similar subjects. As you can see commerce is a more broad course that explores various different areas of the business world. Once you hit 2nd year you can decide from a variety of different majors (accounting, finance, economics, HR, marketing etc). On the other hand economics is specifically focused on these quantitative based eco subjects, it is much more niche than commerce and provides less flexibility.
I would recommend either doing both together (and doing 3 majors) or commerce personally, just for that extra flexibility because you can still choose an economics major whereas with b economics you are limited to a few eco specific majors (econometrics, financial economics etc).
Employment opportunities are pretty grim in the finance industry, it is very competitive and just doing well at uni won't cut it. To get a lot of the top finance roles comm/law is the norm, however more quantitative roles seem to accept students from engineering and maths backgrounds as well due to the analytical skills. Either way, you need killer EC and work experience to land the top jobs.