It reminds me of a well-known problem «mobile app vs mobile website», just like it is discussed here, for example http://erminesoft.com/mobile-app-vs-mobile-website/ I guess the final thought is that all methods have their right to exist and the choice depends on your need.
I see that you look for good explanation of “pros and cons of responsive and adaptive”
I could say that every kind of design is good, but for certain purpose. For instance:
Responsive websites are a good idea if: