Each choice has its own advantages and disadvantages and making this decision depends on several factors, including your personal preferences and finances.

Ownership
Leasing: You don't own the vehicle; you must return it at the end of the lease unless you choose to buy it (which is not recommended due to the total cost involved).

Buying: You own the vehicle once you make the last payment.

Up-Front Costs
Leasing: There may be up-front costs such as first month's payment, refundable security deposit, capitalized cost reduction, taxes, registration or other fees.

Buying: Some of the up-front costs could include the down payment, taxes, registration and other fees

Payments
Leasing: Monthly payments are usually the same as a purchase; the term is shorter since you are paying only for the vehicle's depreciation.

Buying: Monthly payments are usually the same as a lease; the term will be longer because you are paying for the entire purchase price of the vehicle.

Early Termination
Leasing: This is possible at any time, but you are still responsible for the balance of the lease payments (without tax), the original residual value, plus any early termination charges.

Buying: This is possible at any time, but you are still responsible for the balance of the loan (without interest).

Returning the Vehicle
Leasing: When the lease is up you are required to return the vehicle to a location designated by the lender and pay any end-of-lease costs such as; penalties for excess wear and tear or mileage over the agreed upon limits set forth in the lease agreement.

Buying: Not required, when you make the last payment you own the vehicle.

Future Value
Leasing: The future value of the vehicle is predetermined by the lender at the beginning of the term. The lender then assumes all the risk for the vehicles value.

Buying: Since you own the vehicle, you assume any risk of the vehicle's future value.

Mileage
Leasing: All leases have mileage limitations that you negotiate upfront. If you exceed these limitations you will be assessed a mileage penalty at the termination of the lease (so make sure you understand what you are signing up for, the low lease payments advertised in the paper are always low mileage 10,000 to 12,000 miles per year).

Buying: There are never limits to the miles driven on the vehicle.

End of Term
Leasing: The current lease has ended and you must decide to purchase the leased vehicle (which is not recommended) or turn it in (Returning the Vehicle above) and purchase or lease another vehicle.

Buying: made your last payment and you now own your vehicle.

Additional Information 
Leasing: This is not for everyone, so be sure you understand the terms of the lease agreement and ask questions if you do not understand something. Leasing may be a good choice if the vehicle is being used for business, but you should still talk to your tax agency to see where you get the best write-off.

Buying: Although it may take longer to pay off, there are no restrictions for mileage, wear and tear or how you use the vehicle and the money is going towards something you will eventually own.