Leasing and financing solve different problems, and the "right" answer depends less on which is cheaper in a vacuum and more on how you actually use a car. Here's how the two really compare.
When you finance, you're paying off the full price of the car and you own it outright at the end. When you lease, you're only paying for the portion of the car's value you use up during the lease term — plus interest, called the "money factor." At the end, you hand the car back (or buy it for a pre-set price).
Because a lease payment only covers depreciation during your term rather than the full vehicle price, lease payments are typically lower than loan payments on the same car. This is the number that pulls a lot of people toward leasing.
Financing has an end point — once the loan is paid off, your monthly cost drops to zero (aside from maintenance) and you have an asset you can sell or trade. Leasing never ends unless you stop driving a car at all; roll into a new lease and you're back to paying every month, indefinitely. Over 8-10 years, financing (especially keeping a car after payoff) is close to always cheaper.
Leases typically cap mileage — often 10,000-15,000 miles a year — with a per-mile charge for every mile over that at lease-end. If your commute or lifestyle means high mileage, those overage fees can erase the lower monthly payment advantage entirely.
With financing, dings and wear are your problem, but only in the sense that they affect resale value later. With leasing, the leasing company inspects the car at turn-in and can charge you for anything beyond "normal wear" — a policy that varies by lessor and can be a source of surprise fees.
See also: New vs. Used: The Real Math covers the depreciation side of this decision in more depth.