Mtg interest deduction removal vs raising rates

So I was thinking, which one would lower the prices of housing more effectively removing the mortgage interest deduction or raising rates (not saying housing should necessarily be cheaper but just interested)?

I was reading an article a friend of mine posted about the mortgage interest deduction and it got me interested on the topic. The more I think about it the more I think the removal of the interest deduction has the potential to send the system into shock (I.e. Screws up tax planning or now a family can't afford to live there). But higher interest rates have the potential to screw a lot of people who have ARMs.

Both seem to have potential to cause some damage.