These perspectives have very different views of social stratification.
To functionalists, stratification can be a good thing. It is (like everything in their eyes) something that helps keep society stable. It gives incentives for people to try to improve themselves (so they can be part of the upper class). It can also be seen as a way to make sure society runs well because those at the top of the hierarchy will have the greatest talent and ability and therefore should be the ones controlling society.
In the conflict view, social stratification comes about through conflict. It is a way for the elites of society to ensure that people from other classes do not encroach upon elite privileges. In this view, stratification comes about through elite actions to suppress the masses. An example of this might be that American elites (this view would say) ensure that lower classes have poorer education so they will remain poor.