The appearances of Cosmic Armor Superman in comics can be a bit sporadic. You could come across him in specific DC comic runs or special editions. It's best to check with comic book stores or online comic databases for exact details.
In comic vine, it's a tough call. Superman is incredibly powerful, but Batman is known for his intelligence and preparedness. It could go either way depending on the circumstances and the writer's imagination.
There could be a wide range of characters in the 'cosmic watch story'. It might have a young protagonist, perhaps a curious child who stumbles upon the cosmic watch. There could also be an old wise figure, like a mentor who knows some of the secrets of the watch. And of course, there might be antagonists, like a group of thieves who want to steal the powerful cosmic watch for their own evil purposes.
Batman won against Superman because he was able to think several steps ahead. He anticipated Superman's moves and had the right tools and tactics ready. Plus, he knew how to play on Superman's moral code and emotions to throw him off balance.
Batman usually outsmarts Superman. He uses his intelligence and preparation to exploit Superman's weaknesses, like kryptonite or finding ways to neutralize his powers.