The two qualifications are not competing. They are rather complimentary. PRINCE2 gives a very detailed process of managing a project while PMP gives a very detailed knowledge of what project and all the elements of a project. It is good for project managers to have both qualifications.

The best example to differentiate the 2 qualifications is: Soup preparations.

In order to prepare a pot of soup, you need some ingredients like pepper, tomatoes, vegetables, etc. PMP tells you all the ingredients you need to make a success of the soup. PRINCE2 tells you how to start the cooking from step 1 to the last step. PRINCE2 is prescriptive while PMP is descriptive.

Another example is a medical student. They spend the first 3 years learning some theoretical aspects like Biochemistry, Chemistry, Biology, Anatomy, Physiology, Microbiology, etc. The theoretical aspect is the PMP. Then they spend the other half learning how to diagnose and prescribe drugs to patients. This is PRINCE2. A good doctor needs the two; you cannot be a doctor without going through the 2 halves. Which one is better, first 3 years or the other 3 years? Your guess will be as good as mine!
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