The whole payment leaves your account, but part of it repays principal and reduces your debt. Comparing it directly with rent mixes the cost of living with building wealth.
An example with numbers
You pay $900 in rent, or a $900 mortgage payment made up of $350 of interest and $550 of principal. When buying you must also estimate maintenance, insurance, purchase costs and what the down payment could have earned elsewhere.
Try it with your numbers
Set up two columns for the same time frame. Record cash outflows and final net worth separately, including the debt left at the end.
This calculator is on its way. In the meantime, you can do the calculation on paper or in a spreadsheet.
Example figures for learning purposes. They are not a recommendation and do not replace professional advice.