You’re posing an essentially unanswerable question here.
mortgages are not a set monthly amount, or “rate”, in the same way a rent payment is.
A mortgage loan is for the amount of the property than you cannot afford upfront. That could be anything from 95% to 1% (theoretically) of the property value. That will affect how much your mortgage payment is.
You get to choose the term of the mortgage (within reason) so you could choose anything from ten years (large monthly payments) to 35 years (potentially tiny monthly payments).
Once you’ve had the property for a few years you’re likely to remortgage, be in a better position because you owe less now and get yourself onto a cheaper deal.
If you’re struggling on a monthly basis, you can call up to extend your term and thus lower your monthly payment.
After 20-39 years, your mortgage will be paid off and your outgoings reduce again, AND you own a valuable asset. The cost to you was just servicing the loan throughout that time. The rest was going into your asset.
Rent is based on the value of the property and is ongoing into perpetuity. It will never reduce like a mortgage it will only ever increase with market rates. You don’t obtain an asset at the end of it.
So overall it’s very possible to have a mortgage lower than rental rates on your property because of the flexibility of being able to adjust your mortgage term to make it longer for the early years of ownership. It WILL reduce in the future as well because you won’t owe as much AND in ten years time you’ll owe less money, earn more money, and the value of your property will have increased.
So yes. I’d say a mortgage is cheaper in the long run. But “per month” you could make a mortgage cost more than rent depending how you have it set up.