Smaller payment, no money down
New car every 2-3 years
Low miles traveled
Larger payment, with money down
Car is yours, no one can take it
High miles traveled
Those are the most basic reasons for doing one versus the other. Over time it really depends on your life style (and how long you keep a buy and how much money you dump into it) that really makes one choice better than the other.
I personally drive a TON (20-25k a year), so I have to own my cars or be willing to drive the **** out of my Corvette in the summer (to not go over my lease mileage on my "other" car). I did that once, never again.