I know it's super-late and it's also gonna be short and not very pretty, but I didn't want to go two weeks without doing anything. Plus, there's nothing to do at work right now.
Prep
My team's got plenty of information to supplement the descriptions of Ari's characters. Charis and Captain Atom know Midnighter quite well, X-Man knows Quicksilver, and Aquaman knows Sebastian Faust and how Wonder Woman thinks, at least, if not the powers Ari's particular version possesses. Superman-16 is the only true unknown, but they can guess that he at least has Kryptonian powers in addition to whatever "quantum telekinesis" is.
My team is safe from any sort of direct telepathic attacks or manipulation thanks to X-Man and Aquaman, and their psi powers allow the team to keep in constant telepathic contact, as well. Of course, Ari's team would be shielded from direct telepathic attacks and manipulation as well due to Wonder Woman's powers, Faust's sorcery, and probably even Superman-16's super-advanced mind or something.
Unfortunately, Ari's team has the battlefield advantage, since Quicksilver knows Wundagore Mountain extremely well and has the speed to prep the battlefield more thoroughly than my team, although my team still gets its fair share of tech from the High Evolutionary's Citadel, including some lasers and atomic steeds for any Polka-Dotters who can't fly.
Battles
Quicksilver obviously strikes first on Nemesis, but she has her stealth suit's shields up so she's okay. From there it becomes something of a clusterf***, with the ubers and lower classes splitting off into two simultaneous fights.
Ubers
Captain Atom goes for Superman-16 and X-Man goes for Wonder Woman, since their powers seem to match up best. When Atom learns what "quantum telekinesis" really means, though, it becomes abundantly clear that he's got a problem. He can match Superman-16 physically at first, but his energy attacks are either physically tossed aside or absorbed to augment Superman-16.
X-Man, meanwhile, fights Wonder Woman, augmenting his own strength to match hers and using constructs of pure psionic energy to duke it out physically. It doesn't go well, since he's a 17-year-old kid winging it as he goes and she's an Amazon with years of training and experience. So Nate abandons the physical fight and realizes he can match or exceed her powers in every other way. She creates physical psi images, he creates physical psi images to match them. She attempts telepathic blasts and finds them cut off by Nate's shields and vastly greater power. Still, Wonder Woman's scrappy and Nate can't find an obvious opening to go beyond just matching her blow-for-blow and actually take her down.
The ubers regroup and switch partners. Captain Atom holds his own against Wonder Woman, but X-Man runs into the same problems as Captain Atom against Superman-16, since X-Man's powers involve psi energy. Finally, it becomes clear that there is no other recourse but to use the one power Superman-16 can't match: Nate teleports him to another dimension.
Teaming up against Wonder Woman, X-Man and Captain Atom make short work of her.
Others
Nemesis, shielded by her stealth suit's force fields, takes Quicksilver out pretty quickly with her enhanced reflexes and empathic sense to warn her when he approaches. Hardly a big deal, given how often Quicksilver gets knocked out by a clothesline from a person with quick reflexes in the comics.
Aquaman is the obvious choice to fight Faust, but he keeps his distance because his hand can only cancel magic he knows about, leaving him vulnerable to sneak attacks and non-mystical traps the Authorititans may have set up. He uses the laser rifle and atomic steed he obtained to harry Faust from a distance, hoping to break his concentration and keep him from performing anymore spells more than actually hurt him.
Meanwhile, Patriarch is dodging laser fire from the Midnighter using his own atomic steed and his teleportation portals. A blast singes his shoulder and pisses him off, so he teleports the mechanical guts of Midnighter's atomic steed away, leaving Midnighter falling through the air on a chunk of useless metal. Unable to fly and with nothing around for the Midnighter to control his descent with, his computerized brain can't really do much to stop Patriarch from teleporting his arms and legs off, leaving him a helpless paraplegic, bleeding out on the side of Wundagore Mountain. Patriarch still teleports his head away, to put him out of his misery and, you know, just in case.
Aquaman, tired of playing conservatively, shapeshifts his water hand and lets it seep into the earth around Faust, canceling any protection spells he'd set up there. He then rushes Faust, only to find himself knocked back by a purely unmagical mine fashioned from materials in the Citadel. Faust teleports himself to Aquaman to finish him off, but finds himself landing on another teleport portal and winding up in the sky instead, courtesy of Patriarch. While Faust teleports himself again to get back to solid ground, Nemesis and Patriarch regroup at Aquaman's position. Faust puts up a good fight with his magic but ultimately Aquaman's ability to cancel any magic that gets too close, Patriarch's teleportation ability, and Nemesis' fighting skills prove too much for him.
The heroic members of the team--Aquaman and Captain Atom--are upset with Patriarch's actions, X-Man doesn't mind the killing so much as the cruelty of it, and Nemesis doesn't really give a s*** either way. The Polka-Dot Fuchsia Lantern Corps wins nonetheless.