Hacked By RxR HaCkEr
This chart is the simplest answer to both questions.
The longer you rent, the higher the cost, and while you have paid for a place to live, you have nothing to show for it but rent receipts.
On the other side, buying a property to rent has all the advantages the renting does not. In either case, a fixed rate mortgage would hold your costs level (OK taxes might go up, but that's a minor part of the equation), while your rental income increases.
And in both cases, there are significant tax advantages. For Home Owners, mortgage interest is tax deductible. For Investors, you also get depreciation and other deductions. Don't believe me? I can recommend a good Portland CPA.