So, I don't have any experiences with Superman games whatsoever, but I hear every one's been pretty awful, so I don't think I'm missing out on too much. Anyway, here's what I'd do. Eat knowledge.
So, movement's pretty basic. The left stick controls 2D movement. The right stick controls height (up/down) and juking (left/right). The left trigger launches you into high speed flight that would be controlled either with the left stick or with the SixAxis, with how hard the trigger's held down controlling speed. There'd be an auto-lock, with the shoulder buttons switching targets. The direction pad would toggle between the type of target (enemies, pedestrians, objects, ). The face buttons would make up the meat of combat. You'd have two basic attack buttons (an uppercut/juggle and a standard punch), along with a disarm/grab, and a zoom button. You could comfortably operate without the auto-lock, by just using the two sticks to maneuver up to enemies and mixing punches and grabs, but the zoom button would allow you to zip towards whatever is auto-targeted. The trick of combos would be timing the zoom and attack buttons. The speed between hitting the zoom button and the attack button determines the power of the attack. So you could zoom all the way to the enemy and then start engaging, or you could hit zoom and immediately follow it with an attack to wind up the hit, or you could do something in between. Hitting zoom, then the left trigger would have you plow right into the enemy and just keep going into free-flight mode, with the bad guy still in your grip. After grabbing an enemy, you could retarget and just hit the same button to throw them at whatever. So you could throw a thug into another thug, or you could throw a car at a bad guy, or a villain into a building, or whatever. When targeting pedestrians, things would just drop down to grab/drop, while grabbed objects could be thrown with the grab button or swung with the two attack buttons. The right trigger would toggle the face buttons to super powers. Heat vision would use auto-targeting for quick zaps, to make bad guys drop their weapons, to immobilize opponents, to stop cars; freeze breath would stop you in place and use the right stick to control the breath; another button would shoot you up to the top of the map to absorb sunlight when you're weakened. Finally, clicking in one of the analog sticks would activate x-ray vision, which would switch all buildings to wireframes and target on the other side of buildings, thus eliminating the need for a camera system. Clicking in the other analog stick would activate your super-senses. The idea being that if a pedestrian's in critical danger, or a building's about to collapse within the range of your senses, a little inset of the action will pop in on the corner of your screen, and clicking in the button will automatically zoom you there.
Since Superman can take out pretty much any threat if it's just one-on-one, I figured the way to make gameplay challenging (and I'd want my Superman game wicked hard) is to make Superman juggle a lot of different threats at once. It would be a sandbox-style open-world game, with the focus being on epic missions that have Superman dealing with concurrent dangers all over the map. Rather than focus solely on Metropolis, expand it outward. You have Metropolis, sure, but if you fly west along the bay, you'll run into the massive Cadmus Labs facility. Continue down south and you'll cruise down the river to the massive superhuman prison. Go west, and you'll cut through the countryside to find the Metropolis suburbs, the Kansas countryside, and Smallville. Up north of Metropolis, you have the glitzier neighborhoods and Luthor manor. At the heart of it all, you have a sort of "civic health" bar that sinks as property is destroyed and criminals get away with crimes. To complement this, you have certain landmarks scattered across the map such as the Kent home, Lexcorp Towers, and the Daily Planet. The damage to these landmarks does significant damage to the civic health, and if one of them is significantly damaged, it will have more immediate and major impacts. If the Daily Planet's ****ed up then you can't go on Clark Kent missions, if the prison gets ****ed, a jailbreak will occur and balloon crime rates, a damaged Metropolis Police HQ will cripple police in the city, etc. The missions themselves would pit Superman against an overwhelming set of difficulties. Ex: keeping a rampaging Bizarro at bay while you try to foil a series of bank robberies being committed in tandem using the Bizarro as cover, or stopping natural disasters across the map while still managing to arrive at various investigative/interview opportunities as Clark Kent, or simultaneously preventing Mongol's air forces from attacking Metropolis as you try to stem a ground force marching in from the far end of the map. Missions would be scored, and replayable, based on quickly meeting objectives, and effectively setting up smooth combos - setting up a manic, arcade-style system to gameplay. The trick isn't just to complete all the objectives - it's to do it with as much style as possible. It would always be day (just like Gotham should always be night), but would use a clock system that shifted from dusk to high noon to dawn before shifting back through dusk. You have about ten or so anchor missions that are typically intense arcade marathons that take place over the course of a day-in-the-life-of and take about a half hours which typically have Superman facing off against a big-name villain, and smaller missions connected between them that weigh out the game.
As for plot, I'd make military contract competition between Lexcorp and Cadmus the basis for the game, with Superman eventually discovering Luthor has the ship he landed in and recovering it from him. A little ways in, once the learning curve of the civic health bar is surmounted, you introduce a Supes health bar. Early on, these would be rare threats you encounter only when facing kryptonite and magic. But as you dig a little deeper into the game, Luthor's access to Kryptonian technology seeds the production of synthetic kryptonite weapons (an idea that I feel is cheesy in the comics, but would translate well into a video game), adding a new threat to juggle. There wouldn't be an energy bar for your powers, but as your health bar wears down, you lose speed and power. Getting directly into sunlight will slowly replenish your bar, but leaves you immobile while enemies ransack the city. The game would work with sort of a proto-Kirby feel with the Newsboy Legion feeding you missions, and the presence of Cadmus Labs, Intergang, and hints of Darkseid. Luthor's competing with the corrupt Dabney Donovan at Cadmus (which would maybe be called the DNA Project and switched over to Cadmus in a sequel) and eventually starts feeding synthetic-kryptonite technology to Intergang, hoping they'll use it to take down Supes. A number of missions would have you switching back and forth between Clark and Superman, which could be done just by zooming for a phone booth. Clark could jump and punch and work his powers on the sly. The idea would be that each series of missions would introduce a top-tier Superman villain or organization, and have you working both as Superman to disable the threat and as Clark Kent to get the front page story for the Planet.
Onto side missions… The level of crime in the city would be tied to the civic health, and instead of fighting rival gangs, the street crime would all be under the umbrella of Intergang, which increases its toughness and weaponry as you proceed through the game. In free-roam, you could just go around knocking baddies, trying to string together combo after combo, with the threats in the city ratcheting up in conjunction with how well you're doing, and the city healing exponentially the higher you get. You'd have Intergang headquarters and compounds throughout the city changing locations that you could systematically take down, and some sort of side mission that has you directly repairing parts of town that are damaged. You sprinkle in some Newsboy Legion missions and some Clark Kent missions. And finally, you have a half dozen smaller-league Superman baddies who go on semi-random rampages throughout the city. Each one is randomly generated, but follows a basic formula. Terra-Man tears *** across the map on a super-powered rocket, wreaking all sorts of mayhem; the Toy-Man sends armies of robot toys to do his bidding. Apprehend them, and they'll get locked up in the prison, until their sentence is up or there's a jail break. And since the actual process of the missions is fairly simplistic, it would be pretty easy to set up a mission creator system that lets you set up challenges and maybe swap them online.
A sequel would establish a secondary Apokalips map. Follow the same format, with the New Gods as the typical enemies, but some missions boom-tube you to Apokalips, where your health slowly drains, there's no sun, and practically everyone's an enemy. Basically an excuse to put Superman at his destructive best without having to worry about collateral damage. Maybe a second sequel could do the "Death of Superman" thing and have you playing part of the game as four replacement Supermen.