From another perspective, even if not Field Limited on the 6000 ft runway with the "Increased" Takeoff speeds available (Which I assume to be the case as the original poster refers to Obstacle Limit Only), the 12000 ft runway still wins from the obstacle perspective.
Except that when you look in the RPM, the Climb limit on MTOW is independent of runway -- it's a separate column altogether! Therefore, if the controlling factor is second-segment climb, and NOT the runway, then runway length is irrelevant!