Use the same property for both sides - the home's listing price on the buy side, its asking rent on the rent side. Sally buys the home; Jack rents the very same place. Both start with the same savings and earn the same monthly income, so it's a true apples-to-apples comparison.

Sally deploys her down payment plus closing costs into the home and keeps the rest invested. She pays mortgage P&I plus property taxes, insurance, HOA, and maintenance every month. Jack invests his entire starting savings and pays the asking rent each month.

Each month both characters take their identical income, pay their housing cost, and invest the leftover at your chosen return rate (e.g. S&P 500 ~8% long-run). End-of-horizon net worth = invested portfolio (both) + home equity (Sally only).