Cheaper to buy.
All of your rent money is gone. That same amount of money building equity in your bought property stays with you. True, you may need to wait until the property is sold before you see any of that money again, but it's still yours. You might call it 'enforced saving'.
Apart from that money coming back to you, the property you own will appreciate over time. So when you sell finally, it'll be worth more currency units than when you bought it. (That's not really a 'profit', but it looks like one. Anyhow, there's no 'profit' at all when you pay rent.)
