If you purchase the system outright, you own the system and all that it produces. So once you have recouped your "investment" everything thereafter is in the black. Well, there may be some maintenance costs down the road you would have to consider.
If you have lease system, then for a fixed time (mine is 20 years) you get all of the power that it produces. If it under produces, the lease terms specify how you will be compensated. However, it is based on aggregate production so you will only get compensation if there are long-term systemic issues. If it overproduces you get the extra power. Leased systems are usually grid-tied, so if you produce more than you use on average over the course of a year, you can get a check from the utility. Leases vary in that you can prepay the entire lease, prepay none of the lease and have fixed monthly payments, or prepay some and have payments for the rest. The leasing company pays the maintenance costs so your costs on that side are known. When the lease runs out you can have them remove it, buy it from them, or continue to use it for additional cost. It is really hard to predict what the state of art in solar PV will be in nearly 20 years, so I don't know what I'll do when the lease is up. With a leased system the leasing company gets all the government and utility incentives for the power produced, which is why the lease price is low. It is a financially better option to purchase the system but that requires a fair amount of money, which is why leasing is popular.
There is also something called a power purchase agreement that can be used to procure a system. They don't have those here and I don't know whether there is a cap on the amount you have to pay each month.
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