Like Hilarity N. Suze, we had a joint account but different styles drove us crazy. I keep track of pennies, he rounds. I believe in keeping a register, he thinks, “why bother when you can always check online?” In general, though, it’s not a source of tension between us. Lack of money full stop, and earning disparity (me: all vs. him: none) is a HUGE source of tension, but since what can be done is being done we just have to live with it for now.
We each have multiple accounts, here in Canada (both) and Britain (both) and the US (just me) as well as debts. We regularly impersonate each other online with the British accounts, up to and including moving money between them (him > me or me > him). We do clear it with each other before or just after the fact, never been a problem. In general I keep and convey the big picture and he does the daily budgeting.