If your timeframe is less than 7 years buying a house is almost always a bad idea because of the risks. As you get over 7 years odds start to get good that you are even after the downturn (that is the loss in value during the downturn is just a loss back to what you paid in the first place), at which point your house payment vs rent is the only difference, and the foregone gains from the down payment investment. As you get over about 10 years you start to need to consider the costs of remodeling a house, but your rent would almost certainly gone up so again you are roughly even other than the down payment investments. As your get over 20 years rent has gone up again, but your house payment has not and so you are starting to catch up on the down payment investment. At 30 yours rent has gone up again, but the house payment is gone and you can really work at that down payment investment difference. At 40 years both retire, the renter has still more rent increases which need to be paid for from that down payment investment. AT 55 years both move to assisted living, the renter just sees another rent increase, while the homeowner sells the house and has a big influx of cash that should take care of rent until they die. Ideally both give their last 20 to the taxi outside the hospital 20 minutes before they die. The renter's highest investment balance was higher than the homeowners, but the renter had larger expenses latter in life and so had a bigger draw down of principal.

There are a number of assumptions in the above. Each that is different for you changes the analysis. In particular it assumes disciplined savings such that rent+savings == house payment + house maintenance + savings. It assumes that house maintenance and remodeling is not making the house more luxurious. Its assumes similar levels of luxury (renters are likely to go for a cheaper apartment and spend the difference in housing luxury on travel).

As always, location, location, location. Different areas have different situations that can make one significantly worse than the other.