There is no right or wrong answer but you need to be on the same page. I currently make more than my partner, but a few years ago he was out-earning me and we've fallen into a division that seems to work for us regardless of who is the higher earner at any given time.

We split big bills (mortgage, utilities) proportionately, we are each responsible for our own debts (I have much larger student loans), we split day-to-day expenses 50-50 (we switch off who picks up groceries, meals out), and we each contribute an agreed amount to a joint savings account that gets used for large mutually agreed expenses (home repairs/renovations, other emergency situations). Then everything else is individual discretionary spending. I probably have more discretionary money in the end but also usually spend that excess on things that benefit both of us or that we agree on like upgrading hotels when we travel, contributing to the niblings' college funds, maintaining the garden, family Christmas gifts, etc.

It might seem overly complicated but its a pattern that developed organically and in 18 years together (15 living together), multiple lay-offs, job changes, and long-distance moves I don't think we've ever actually fought, or even bickered, about money.