I don't believe there is a difference, at least in the case of AA and AS. In fact, I would put CO in the same category as you can redeem CO miles on AS. In making arrangements to vacation in Alaska next year, I checked AA, CO, and AS for award availability on the same AS flights. I was told by all 3 airlines that the award pool was determined by AS (since the flights are operated by AS) but that all 3 airlines had the same access to the award seats.

With different airlines the situation may be different. Elsewhere on FlyerTalk, it was revealed that Hilton had more award seat availability on certain UA flights to Hawaii than UA itself! I guess the answer is it depends on the partners.