The major difference between these two systems is that in a Presidential system, the executive leader, the President, is directly voted upon by the people (Or via a body elected specifically for the purpose of electing the president, and no other purpose), and the executive leader of the Parliamentary system, the Prime Minister, is elected from the legislative branch directly.
In the Presidential System, it is more difficult to enact legislation, especially in the event that the President has different views than the legislative body. The President only responds to the people, the legislative branch can't really do anything to threaten the President. As a result, he can make it more difficult for the legislative body to do anything.
In the Parliamentary system, if the Parliament doesn't like the Prime Minister, they can cast a vote of no confidence and replace him. This tends to make the executive leader subservient to the Parliament.
Bottom line is, if you believe that government should have more checks and balances, then a Presidential system will give you that. If you believe that it should have the power to enact laws quickly, then you should go for a Parliamentary system.