As Lefty alluded earlier, to more HOF's, that just proves a point of a more competitive history between the teams. Both organizations are ranked #1 and #3 in organizational wins all time. Both are separated by only one World Series(7-6). They've played over 2300 games against each other, the Giants barely lead 1190-1166. You realize how close that is in over a century given span?
Your also, not going to find a rivalry with as many back and forth spoilers. Both teams denying the other of pennant chases countless times. Coaches, players denying trades to play or coach the other's teams. Players hitting other players with bats. They've been cross town/cross state rivals since 1880.
Definition of Rivalry:Competition for the same objective or for superiority in the same field.
Your not going to find a closer rivalry than these two teams.