I think the relative amount of influence both groups have is summed up by what would happen if they disappeared overnight. If TB vanished, then FlyerTalk would continue to function. If the mods vanished, then yes, it would continue to function, but the larger, higher volume boards would get more and more acrimonious, and there would be a lot more spam threads to deal with - in short, the user experience would be a lot worse, relatively quickly.
Why are the mods not elected? Because mods shouldn't be appointed by who is most popular, but by who can do the best job - which does sound a very bizarre thing to say since I've put myself up for TB
But since I do think I can do the best job....