This is important. If you're merely a mortal with a few powerful spells, well that's not very different from standard RPG fare. At the same time, PCs can't be truly omnipotent, or there would be no meaningful challenges. There must be a happy medium between powerful mortals and truly omnipotent creators-of-universes.
In the game I played (referenced a few posts back), it was basically a superhero game in disguise, not unlike the Avengers. Big powers that could change worlds or even the universe, but nobody had all the power. Each god had a portfolio or powers and alliances and relationships with other gods. There was lots of politicking, some mega battles, etc. The gods were effectively invulnerable to most mortals, though we all had weaknesses and vulnerabilities that could be exploited. We were mostly "good" gods, so we spent a lot of time trying to minimize collateral damage to mortals. As far as I can remember, though, there were no mechanical elements to enforce this. (Though it was clear that you couldn't buy off your core disadvantages. If you had a weakness for wine, that was a fundamental part of your divine nature.)
It might be interesting to play around with mechanics behind the scenes. In some RPGs, there's been the idea that you get your power from your worshippers. In a game with that premise, you would want to gain and retain worshippers to maintain your power. Some might do this by being nice and friendly and whatnot. Others might use fear or threats. (I don't know about the psychology of all of that, but within genre, it seems plausible enough.)
I've never thought that the worshipper thing allows for quite enough diversity, especially on the "evil" side of things. Maybe there's a customizable goal for each god that their powers depend on. If you're the evil god of rotting filth, you maintain your power by spreading disease and setting loose fungus hordes and whatnot. Meanwhile, an opposing god of wholesome nature will attempt to block your blight. Crafting these goals in interesting ways could provide motivation for divine-scale adventures. In your premise (demigods in the modern world), the PCs might need to preserve the independence of mortal life and defend against incursions by opposed deities. (Which might end up resembling a Secret Magic / Monster Hunters campaign.)