I just don't think there's a fight to win. People will play both, and both may end up being successful. I imagine there's a good chance people may end up playing both at the same time.

I'm not worried. The fact that, like you said, both games offer something different should be enough to not make anyone worry. Personally (though I'm really enjoying Skyrim) I'd never touch an MMO based on TES. I don't like the world, I don't like the combat, and it's all so... western? I'm not sure if that's the right way to put it, but it's how it feels. ARR may be influenced by more western MMOs, but it's still a final fantasy, and it's a love letter to past final fantasies on top.

Both games will have healthy populations.