Monthly cost of a house tells you very little about the "true cost of ownership" (a concept that I wish were taught more widely). That includes things like taxes, opportunity cost of capital, maintenance, etc. Doubling the price of the house will not quite double the TCO (because maintenance may not increase by much depending on various factors, and taxes can take time to catch up), but it will not be a mere 25% increase either.

This comparison of an increase in price and decrease in interest rate is not useful because if interest rates come down, mortgages can be refinanced at the lower interest rate.

The 100% more expensive house actually costs 100% more (nominally).