If you go here: http://www.forbes.com/pictures/mlm45eidmk/1-new-york-yankees-5/
You'll find the operating income for each team (These are 2012 figures, since 2013 is under way). That's the true "revenue" that is earned from operating the team (after tax deductions, player expenses yada yada yada). The Red Sox had a 23.9 million operating income last year. This is inferior to the Cubs, Nationals, Astros, Orioles, Padres, Pirates and A's. The Yankees are a wild-card because no one knows exactly how much money they make from the YES network, but 2012 was not kind to them either way. The Angels and Dodgers join that team this year, and will certainly have a higher operating income than the Red Sox.
Also, you can reasonably assume that the Red Sox' overall operating income was boosted by the Dodgers deal, and you'll notice that smaller market teams with more conservative payroll inclinations are making more money overall than some of the big spenders. The Red Sox don't have infinite money. That notion, and the notion that they are cheap, is flat out incorrect.