As someone that has been exploring real estate for the first time, after speaking with some people it seems that mortgages have generally been less expensive than rent? Good luck finding something like that with today's prices and interest rates.
That said, if you have rent control locked in, the choice is likely easy.
This is very location-dependent. In some cities it is true, it some it isn't, in some it depends on the segment of the market.
However, you can get "trapped" as I did if you bought near a high point, and then interest rates and prices dropped, and since I was now "underwater" I couldn't refinance, even though I was perfectly capable and did continue to pay on the original loan. Eventually the property appraised high enough to refinance again.
That's not the case for refinances after Jan 1, 2013.
There is no particular reason to believe rates will go down again. They might, they might not. Historically todays rates are around the normal low.