No offense to Penn, but I've never heard anything about their theater department.
OTOH, Northwestern's theater department is one of the finest in the country. I think NU and Penn are similar in many, many regards, but in this area, how is there possibly any comparison?
And to your question of identity - theater matters greatly to the spirit of the NU undergraduate campus as a whole, even to the non-theater majors. Everyone goes to the plays / shows, especially Waa-Mu, which is a tradition that unifies the campus.
You can hardly watch a major TV show without seeing an NU alum be prominent.
Plus, it elevates the looks of the student body. Ha ha.