I'm not sure there are any websites that compare cost of living prices directly, but from my experience here, I'd say that Qatar is slightly more expensive. While housing prices are what you might expect to pay in the bay area or LA, the size of the apartment or villa is generally much larger. Renting a car is certainly cheaper - about half the price that it would be in the states. Dining out is very expensive (by a factor of 1.5x to 2.5x) and coming from California, don't expect to be to excited about the selection of fine European/western restaurants here. On the other hand, if you feel adventurous, there's a plethora of inexpensive and very tasty Mediterranean and Asian spots.