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Both turn equity into cash, but they treat your existing mortgage very differently. A HELOC (or home equity loan) is a second loan that leaves your first mortgage untouched. A cash-out refinance replaces your whole mortgage with a larger one.
The rate question decides it
If your current mortgage rate is low, a cash-out refinance would reset your entire balance to today's higher rate — usually a bad trade; a HELOC keeps your cheap first mortgage and adds a smaller second loan. If today's rates are lower than yours, a cash-out refinance can lower everything at once.
Model both with the cash-out calculator and HELOC calculator.