One point to offer to the rent payment vs. mortgage payment point you make is the mortgage payment is not all there is to home ownership. This is sometimes presented to the prospective buyers as a principal and interest payment only. The property tax and homeowners insurance numbers are left out of the equation.
Typically you get a number, PITI. THAT is the number you work with, not merely the principle and interest. Both times I have purchased a home, that is the number the mortgage people gave me, then pre-approved me for a certain amount based on the monthly PITI.
It's pretty simple to run the numbers and compare it to your income, what you're currently paying for rent, what you can afford to pay, etc. If you currently pay $1000/mo for rent and are strapped, you cannot afford a $1500/mo mortgage. Simple.
Again, if you read the sob stories about people losing their homes, you'll find a lot of A) investors; and B) people who felt the need to buy new cars, furniture, trips, etc, in addition to their new home. They could have afforded their mortgage just fine until they racked up $20k in credit card debt.
Like this one family, and I think the link is actually in this thread somewhere. They're whining about foreclosure while their children are going to some fancy private school, they drive around in luxury automobiles, and are doing all their grocery shopping at the Whole Foods. This is not a family who over-bought their home - they are overspending on other things.