Alright here we go:
Either two separate teams, or one team whose goal differs depending on your version. I'd prefer the latter because I don't think a "Magma vs. Aqua-esque showdown" is particularly interesting, especially when they're both bad guys. If one of them is good, at least that's interesting because it shows there are people out there willing to stand up to take down the bad guys, instead of just leaving it all to one kid. But that aside...
Sun: When people sleep, they aren't productive. We could be getting so much more done if we never slept. Our goal is to make it so that nobody is ever able to sleep again!
To enhance this, have certain major characters such as scientists and professors reiterate on important occasions that their technologies could be so much further along if there was more time to work on them, etc.
To conclude this, the "moral" would be that instead of losing sleep (literally) over your goals, plan them out and if you can't quite reach deadlines that's okay, just keep doing your best, etc. etc.
Moon: People are awful! All they do is hurt each other and take from each other! Our goal is to place everyone into eternal sleep so they cannot be evil any more.
To enhance this, have there be many notable "bad" NPCs (not from the evil team) who steal, vandalize, bully, etc. Even small details such as accounts of numerous (not just one) recent major conflicts can make it seem like the team has a point--people really are out of control. Instances of poverty and lack of resources can help, too.
To conclude this, admit that there can be bad in the world, but punishing everyone isn't the right way to fix the problem. A little bit of kindness goes a long way, and can encourage others to be kind, too.
This can offer numerous NPCs various growth opportunities: in Sun, coming to terms with their own weakness of being unable to plan around the fact that people need rest, sleep or otherwise, from their work in order to perform their best; in Moon, learning to remain positive and kind towards others even when others aren't kind to you--or admitting your behaviors are wrong and learning to perform kind acts. Just as some examples.
Perhaps the legendaries will have abilities or attacks in relation to this: the lion regarding waking up/staying awake, and the bat regarding falling/staying asleep (some people have mentioned that its appearance is similar to a dream catcher's).