If I remember correctly, both Bahamut and Odin have been referred to as Elder Primals. What makes them Elder? Is it just that they are more powerful than the "lesser" primals? My first thought was that maybe they interact with aether in a different way without the need for crystals to be summoned. This would mean that they don't have to influence Eorzean followers into gathering crystals leading to the possibility of them being unaligned with a tribe. The dragons could have started worshipping Bahamut because he is a dragon instead of him needing them. Of course that leads into how the beast tribes came to worship any of the primals. Were the primals at one time loose in Eorzea and then later banished?

Back to my original point (what makes elders special). Since Bahamut was actually sealed within Dalamud, he has been physically manifest since Allagan times. Maybe the length of time they have been manifest is what makes them elder. This would mean that Odin has also been hanging around for a long time. That would also work for the whole scaring away the Garleans before the summoning started.