The large number of meetings of these two teams owes more to their longevity and the circumstances of earlier eras of MLB than any current lack of parity among franchises. The Dodgers have been around since the late 1800s, the Yankees since 1903.

Since 2003, the Yankees have been to two World Series. In that same span of time, the Dodgers have been in three. Three other NL teams have had just as many WS appearances as LA in those two decades: the Cardinals, the Phillies, and the Giants. Six AL teams have had as many or more WS appearances than the Yankees: Boston, Houston, Detroit, Tampa Bay, Kansas City, and Texas. It should be noted that the Astros have had five total WS appearances in that time, with one in 2005 representing the NL before they moved to the AL in 2013.

There have been eleven teams other than the Dodgers who won the NL pennant in the past twenty years. There have been eight AL pennant winners other than the Yankees. MLB currently has thirty total teams split evenly between the NL and AL. Including the Dodgers and Yankees, the NL has been represented by 80% of its teams in the past twenty WS, and the AL by 60%.

Judging by WS appearances, there seems to be reasonably good parity, and there is no evidence of strong bias towards either of the teams in question.