Replacement cost of a house is typically way more than its purchase value.
Every property is the value of the lot (land) plus the depreciated value of the house, unless it happens to have some enhancing story line value or is a renovation of what was upscale materials.
When building a home, if not putting in labor yourself, and having a contractor do it, it has to cost more, and extra if it is a custom build. There are times that a cookie cutter high volume builder can get enough materials discounts to sell it at extra value as a rare exception. There are manufactured pre-fabs that can be a value, or semi-manufactured, put together quickly.
New homes are usually where the land is cheaper, and existing homes on more valuable lots, and that balances the price. But, the general statement is that existing homes are cheaper.
It's always cheaper to buy an existing structure than to build something equal to it.
Depends where you want to buy, and the kind of house you want to live in
Land can be very expensive, so you'd need to take this into account
depends on how much the land cost, and how much of the work you do yourself
***IN GENERAL*** it is cheaper to buy a pre-built house. Usually, the value of a finished home is less than the cost of the land and construction. This is why banks require a higher down payment for construction loans than home mortgages. They know that the value of the finished house is probably less than the amount you borrowed.
Also, unless you can pay for the land and construction, you will be paying financing costs during the construction, which you won't have if you just buy a home. Finally, you have to consider that you'll be paying to have a place built and taking on the risks of construction while still paying on your current house during construciton.
It's the cheapest to build it from ground down. Underground is the future