[Yeah, the choices seem primarily to be two of the big teams. There isn't really any other one to go with, unless you wish to stay neutral in the situation. There's a small group here or there, but they typically disband as quickly as they form, such as the bear group.
Aether touts more "experienced" members, which isn't a lie, and Bismuth touts having more of an actual goal. I'd be surprised if Aether was beat by Bismuth in knowledge, to be frank, but honestly they seem to be more a loose confederacy than an actual team. Bismuth on the other hand does have an actual goal, but I'd wager less members as well, and probably less of a robust knowledge foundation. Aether has more experience in the intricacies of magic, how it can be used, but Bismuth, once again, seems to actually have an idea of how to apply such knowledge.
Another thing is that Aether would probably be considered the more "vicious" team, as prior experience tends influence them, and a show of strength can be comforting to its members, as fear does tend to influence those that go against such. Bismuth is more the "generous" team in that they seem free with their resources, more apt to want to make alliances and contracted friends than enemies to crush. This can be a comfort too in another sense.
I'm sure both teams are probably strapped for members, at least not as much as they like, if they campaign this hard and keep so tight lipped about numbers. Otherwise, if they were secure in such knowledge, they'd put it as a focal point, an appeal to ad populum so it were.
Really, if Aether were to consolidate and coordinate their resources and members, and work up a goal, they'd be a stronger force to be reckoned with than they already are, which by itself is already something. Likewise, if Bismuth were to beef up their knowledge and experience and have a bit more coordination between the members it would be the same story.
At least, this is an outsider's perspective.]