Ignore everyone being too cool for school in this thread, it's the Cubs without question. It's a derby, it's the most attended series every season, it's the loudest the Cell will be all year, the media will preview it more than any other series. Rivalries are about the fans, and the Cubs are the rival the fans care about most.
When the Sox are competitive, rivalries between the divisional teams start brewing again, but at times like now they are pretty dormant. With the new schedule format, each divisional team is faced 19 times, so it's hard to get too excited for a particular matchup if you aren't fighting for the postseason, especially when each team will win minimum 4 or 5 of those games given the nature of baseball.