The MFJ vs MFS form shows immediately the difference in tax liability, joint vs separate. For Ohio, it also shows the difference for the state and for the combined liabilities. Because OH begins with AGI and limits deductions and has other differences, it is possible to owe IRS but receive much larger, offsetting refunds from the state. Your situation may vary considerably. Just be sure to note the liability difference, not whether tax is owed or refunded. That depends on how much tax was withheld, of course.
To date, even with 'warring' couples, none have chosen to pay more tax overall just because the withholdings were not aligned. A fairly recently married couple, older, was very surprised at the significant difference it made as a household liability. Neither had been previously married and wanted to keep everything separate until it would have cost them, combined, over $1000.