I've done a good amount of testing, and I think it's safe to conclude that the faction standings at a given aetheryte determine how many faction credits you get for completing a leve. If you do a rank 20 leve, for example, it will break down like this:

1st = 4 credits
2nd = 6 credits
3rd = 9 credits

Things to note, if you want to test this for yourself:

-Faction rankings vary from aetheryte to aetheryte.
-When choosing leves, you can back out and re-select them to change the faction they are associated with.
-Faction rankings at an aetheryte can change in real-time(It's probably safe to assume they change as people do more or less leves associated with the different factions).