Perle is saying, "let's learn the music, love the music, become one with the people and places (social context) behind the music, and let the music tell us what it is about."
Forte is, rather, creating a general theory of music out of pure number relations, and then saying, "let's apply this theory to a given corpus".
It is really ideology that creates the "gulf fixed" between the two. The music is the same, and the application (note crunching in one way or another) is in many respects similar. Perle is in the same ideological boat as Schenker, defining a canon by cultural context, elevating it, and then attempting to demonstrate it's qualities of genius and uniqueness. Forte's theory (in theory) could apply to any music.
All of which, like it or not, will eventually lead us in to the synthesis--the grey--of David Lewin and his Generalized theory, in my opinion.