I assume that you are talking about Packer's models of the criminal justice system here. If so, the major difference between the two is in what they are each really trying to accomplish. The crime control model is trying to reduce crime while the due process model is trying to protect the rights of the accused.
In the crime control model, the idea is to reduce crime by almost any means necessary. The police and the prosecutors should be given more powers to pursue criminals or potential criminals. This would reduce crime.
In the due process model, the idea is that the people's rights should be protected from the government. This model believes in curtailing the powers of law enforcement to keep them from trampling the rights of the people.