The downside of leasing is that you don't own the equipment, and therefore, you can't use it as collateral for any loans. Leasing is almost always more expensive then buying over a period of time. But if you are short on cash, and you need to equipment, leasing is the easiest way to obtain it.
The upside is that the lessor of the equipment will usually take care of maintenance and repairs. Lease payments can also be deducted as business expenses.
A point to remember when leasing equipment: The longer the lease, the smaller the monthly payments. Check to be sure that your lease covers service of the equipment and what the terms of that service are.
Before buying equipment, do a little research on leasing. Figure up the total amount it would cost you for the length of the lease, including finance charges, sales tax, etc. and compare that amount to the total purchase price of the equipment. You will then have to decide which route is best for you and your business.