as per my experience, the individual FFP will give more perks to their own members.
This is to promote people to fly with their FFP partner airlines.
For example Flying Blue Silvers can enjoy SkyPriority at check in and during boarding when flying FB partner airlines. At AMS Silvers also can use Fast track security. Normally these would qualify as Elite Plus benefits.
When flying with other sky team members, they have normal elite benefits.
In your case DL elite on MU gives no skypriority. In my case MU elite gives me skypriority+lounge on MU, but not on DL.