Why add extra variables like down payment and principal to this comparison. It would only give more room for error. How about we compare a $600k house/th/condo using I/O loan and 0 down.
On a $600k IO loan, the monthly interest would be around 3400 in the first 5-6 years of ownership.
$3400 Interest
+$625 Tax
—–
$4025 Before tax saving.
$2656 after tax saving.
+$200 HOA
+$100 Insurance
+$100 Repair, etc. (low estimate)
—–
$3056 After said and done.
$2350 Rent average.
—–
$700 Overpaid per month = 30% more than rent
With $700/month saving, if you invest it and get 7%, in 10 years, you’ll have $121k, @ 8.5%, you’ll have $132k, @ 10%, you’ll have $144k.

That mean your house has to increase by 20-25% over the next 10 years in order for you to break even.