With the owned airplane you will be responsible for managing it, which adds to the already large cost and effort of getting flight ratings. While owning a trainer is never a bad idea, saving money is not the advantage assuming there are similar rentals around. You can save more by flying less hours, which is under your control. The reason to buy one would have more to do with intending to use it after getting trained to fly it. This is especially true of high performance airplanes where the intention is to use it for business. For the average trainer there is no great advantage to owning it. There may actually be some disadvantage in the sense that otherwise you would be exposed to a wider variety of aircraft.