Either works. The IRS treats withholding as paid evenly through the year, so raising it can replace quarterly payments and even fix a late start.
Both routes get money to the IRS during the year, and the IRS accepts either. The difference is how each one is credited. An estimated payment counts for the quarter it arrives in. Withholding is treated as paid evenly across all four quarters, no matter when it actually came out of your pay.
That timing rule is the lever. Raise your withholding in November and the extra is credited as if it had been spread across the whole year, which can erase a shortfall from the spring. A quarterly payment made in November only counts toward the fourth quarter.
Withholding is usually the better tool when you or your spouse has a W-2 paycheck to withhold from, when you want one less thing to remember, or when you are behind and need the even-spread rescue. File a new W-4 with your employer and put the extra amount on line 4(c).
Quarterly payments are the better tool when there is no paycheck to withhold from, or when your income arrives unevenly and you want the annualized income method to size each payment to what you actually earned. Either way the target is the same. Reach the safe harbor amount and no underpayment penalty can touch you.
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Sources: IRS Publication 505· Form W-4