The difference is, Superman has a long internal struggle between his desire to do right and his desire to give up in the face of so many people suffering, he may be America’s Boy Scout but he works hard and he keeps a low profile and he is modern day Sisyphus - skipping out on his everyday life to go to unpleasant places alone and deal with unpleasant people, save lives, and come back to .. a journalist notepad and a story about some trivia and no amazing rewards.
Neo on the other hand is a modern day superhero exactly, he’s like the Wanted film main character - he did nothing, doesn’t work hard, doesn’t train at anything, and then sometime while he’s working a drudge job and slacking off, the universe dumps hero on him because of someone he innately is, and then everyone loves him for this thing he didn’t do, but instead is a thing he is.
The equivalent in real life might be considering Dr Jonny Kim, graduated high school, joined the navy, became a Navy SEAL, became a combat medic, sniper, navigator, went on 100 combat missions, graduated with a math degree, went to Harvard med school and became a doctor, and is now a NASA astronaut selected as a possible mars mission candidate, navy reservist, husband, father, decorated combat vet, and 35 years old; and then imagining NASA deselecting him and replacing him with a 35 year old you know who “thought about being the first man on Mars since childhood” and whose favourite film is “The Martian”, and is just waiting for NASA to find him because he’d be the perfect candidate, he could “learn any of that stuff but won’t waste his time until they choose him” [hey that too much describes me!]. Sure maybe Jonny Kim always dreamed of going to Mars and loves The Martian, but he also did things.
Batman went to be Far East and trained hard in martial arts for years, Neo waited for someone else to load martial arts skill into his brain in a safe virtual environment which he could control so he never lost.
Heroes in the past did hard heroic things, rather than dreamed of being called upon to do easy heroic things they could innately magically do. Heroes of the past wanted to win a war, action movie heroes play to a viewer who wants to be seen as a hero and doesn’t care how the saving of people (or whatever) is irrelevant and secondary.