Its heavily market-dependant, but assuming rent expenses = the cost of interest, from a financial perspective they are close to equivalent. If you take the money that would be paying off the mortgage to invest, you should be in a similar financial position at the end.
1-1 compariaons are hard, though, because in practice houses are huge levered bets on a RE market, so they can have huge returns if chosen well. Those are usually the kinds of markets where rents tend to be lower than the mortgage payment, however, so things might net out more even than you'd expect at the end.
Depends on the country I guess. Mortgage interest in AU is not tax deductible unless it's an investment (ie. owner-occupiers don't get a deduction). Consumption is not generally tax deductible, was my understanding (and living in a house is basically consumption)
Its heavily market-dependant, but assuming rent expenses = the cost of interest, from a financial perspective they are close to equivalent. If you take the money that would be paying off the mortgage to invest, you should be in a similar financial position at the end.
1-1 compariaons are hard, though, because in practice houses are huge levered bets on a RE market, so they can have huge returns if chosen well. Those are usually the kinds of markets where rents tend to be lower than the mortgage payment, however, so things might net out more even than you'd expect at the end.