I have 22.3k boss points on my main character, and I have the same feeling as you: it seems like the extra chances of dropping something rare don't make the slightest difference.
But it's about luck, especially since it wouldn't make any sense for certain characters to receive special treatment. And I think that, with some bosses, certain vocations have an extra advantage in dropping something rare, either by dealing and/or receiving more damage. For example, I killed more than 150 King Zelos with my MS and ED, and only dropped 1 rare item. EKs and RPs, on the other hand, were usually the ones who frequently dropped something rare. CipSoft never gave many details on how the participation system works, so this is just a perception I've had over the years. I had a party to kill bosses for a few years, and it was noticeable that some players always dropped more items.