“Who would win in a fight, Superman or Batman?”
I wish I had a dollar for each time someone has asked a question like that.
The answer to any “Who would win in a fight” question is typically on the cover of the comic, movie, or book. If it says “Superman,” he will probably win. If it says “Batman,” he will probably win. Get the picture?
The modern incarnations of Superman are troublesome in storytelling. How do you find an interesting threat for a character who is super in every facet of his being: strength, speed, senses, flight, intelligence, muscle control, he can freeze things with his breath, and shoot deadly beams from his eyes, and he’s even super good with his personal relationships. He has no real faults.
The answer to this problem is frequently one of two options:
Option 1
Make a bigger, badder, nastier villain. This has been used over and over again, and most of the time results in a boring slugfest that is ultimately unfulfilling.
Option 2
Lower Superman’s powers without saying anything.
This happened all of the time on the Justice League and Superman animated series (which I love nonetheless). Often times in Justice League, a villain would kick Superman’s red and blue ass (establishing the villain as a nasty threat) only to have Hawkgirl snuff him with her mace. It just doesn’t work. In this case, Superman is only as strong as he needs to be in order to resolve the conflict after getting beat up a bit.
Superman is problematic because he is a god in a world of mortals and writers have to resort to odd or inconsistent storytelling in order to manufacture a threat. For example:
Think back to the movie Superman Returns. Supes is on that kryptonite island with Lex and his goons. He can barely stand. They stomp on him, stab him with a shard of kryptonite, and dump him in the ocean broken and defeated. Then, after a brief recharge of solar energy, he flies down and lifts the whole damn island into space. The island made of kryptonite. He could barely carry his own weight while standing on it, but lifting it beyond Earth’s gravity is no big deal? That’s bad storytelling.
There is a relatable and interesting character deep within Superman, but it is buried beneath all of the powers. DC could make Superman into an exceptional character if they dampened his strength and speed for good. If he becomes weaker and slower, writers could keep his power consistent, more villains could pose a threat to him, and the crux of his stories could be character-based, not strength based.
The endless strength and speed may be good for beating up bad guys, but they aren’t so good for compelling storytelling.
The Geek Whisperer 
I think Superman will win. He is just the best superhero ever.