Jenny Q and the Doctor erase them all as soon as the fight starts... Or the fact that both Jennys are in the same place ends the universe or something, killing both teams.
Provided that the universe stays intact, the Authority wins, all day, every day.
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Usually the planet-threatening kind. If they only have enough power to take out, say, a continent, they're pretty low power.
A few that come to mind are "God" (a continent-sized being capable of terraforming the planet in mere hours), an assembly of hundreds super villians spread out over the globe, a telepath who siphoned strength/durability/healing powers from over half the world's population, Seth - a super being with more super powers than there are names for them, and all sorts of reality-altering or planet-destroying alien types.
None of the villians are recurring however....the Authority usually just kills them rather than let them live. But their villian set is basically the JLA's or Avengers' on steroids.
They also fight "real-world evil" like corrput government regimes and stuff like that. It's not really a fight, but they like to take the fight to the bastards who normally slip under the super-powered radar (metaphorically speaking).
You'd really need a marvel team with people like Silver Surfer, Quasar, Doc Strange, or Thanos to stand up to Jenny Q. and the Doc. Nerfaria's a good start though. Cloak too. Don't forget Cloak.
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