The benefit of having you own rent a car is that you can go from place to place when you want and you have total independence. If you intend to drive around to the sights and not trek much then a car may be a good option, especially if you are four or more people together.
The unseen disadvantage to renting a car is that unless you use it each day you will be paying for something when it is in the car park, as it may be for several days if you are trekking in Torres del Paine. And if you are trekking you will have to leave it in one place, but then need to get back to that place after the trek, which may require a private transfer to get you back to where the car is. It also costs money with petrol (gas if you are from the United States) and there is a fee to pay to take it across the border to Argentina.
ExperienceChile.Org can arrange rent a car from Punta Arenas, El Calafate and Puerto Natales.