I just feel like Pursuing My True Self ties in better to the overall story than Shadow World does.
Dont get me wrong, I know they both have similar lyrical content, and like you said, Persona 4 is all about friendships, and Shadow World portrays that really well. But Pursuing not only has that, but also encompasses the themes of media influence and, as evidenced in the title, being true to oneself.
Not to mention friendship is not the central theme. Friendship is important to P4 but the main theme is definitely seeking the truth rather than accepting a convenient lie. Shadow World does touch on the truth thing but more in a general sense. The original theme makes it more about the truth of the self.