depends.
$500 a week rent is just that - money in someone elses pocket. But you don't have to fork out extra for water rates (yes sometimes you pay excess but not the actual water rates), council rates, building insurance, maintenance (ie if something breaks you ring the RE and the bill goes to the owner).
$500 on a mortgage is investment in your pocket, but it doesn't cover all of the above, it's extra.

We rent and own a home. They are in different states so I don't have a great comparison, but for what rent is worth here I couldn't get what my mortgage affords me.