Is it Buda or Pest?

Excuse me, could you clarify something for me? In the context of discussing the two halves of Budapest, I've heard it referred to as Buda and Pest, but I'm a bit confused. Is it Buda or Pest that is the more historic and cultural side of the city, or are they both equally significant in that regard? I'm trying to plan a trip and want to make sure I don't miss out on any of the must-see attractions.