The decision to lease or rent a car is very personal, as it depends on your individual situation. There is no simple answer that will be right for everyone. Think about how long you will need the car and what you intend to do with it -- travel or emergency use, for example.
The two methods of obtaining a car do share some similarities, because both involve arrangements that are not permanent.
If after all of this, you still can't decide which option is right for you, then you may be stuck between wanting a short-term rental and a longer-term lease. The answer in this case may be to simply buy a used car you can afford with cash, as it might be cheaper than either option in some situations.