Let us turn back the clock to the beginning of the 2004 baseball season, before the Red Sox ended their curse, and look at the longest droughts in professional sports at that time.
NL World Series : Chicago Cubs, 1908 (last Boston Braves series title : 1914)Since the start of the 2004 baseball season, the Red Sox (twice), White Sox, Bruins, Blackhawks, Patriots, and Celtics have all won titles, as have the men's ice hockey teams from Boston College (previous in 2001; 2008, 2010, 2012) and Boston University (previous in 1995; 2009).
NL Pennant : Cubs, 1945 (Boston Braves : 1948)
AL World Series : Chicago White Sox, 1917 (Red Sox : 1918)
AL Pennant : White Sox, 1959 (Red Sox : 1986)
Stanley Cup : Chicago Black Hawks, 1961 (Bruins : 1971)
NFL : Chicago Cardinals, 1947 -- even moving away from Chicago did not help them any (Patriots won the Super Bowl after the 2003-04 season for their second title in three years)
NBA : Celtics 16 titles (last in 1986), Bulls 6 (last in 1998) -- however, the Bulls had not made the playoffs since their last title
I still don't see how Boston could be more cursed or starved than Chicago.