I think that the worst way to write a superhero story is to think of it as a genre and stick to a classic formula insted of adding something new to the mix, let me explain.
Superhero stories can lend themselves to be little bit formulaic, you know, guy gets powers, learn to use them, villain appears, they fight and the hero is defeated, the hero doubts himself, they fight again and finally defeats the villain in turn.
Of course you can keep to that formula and if you write a good conflict and good characters it would be able to fly with no problem. But I think that the best way to aproach this kind of stories is to look for fragments of others genres that could give a mor unique feel to your story.
I think the best superhero stories are done when they mix it up with others genres and don't try to be a classical superhero story. For example, Thor is a superhero who lives in a fantasy world with a lot of political drama or Spider-man have a lot of romance and family drama. The X-men during the classic Claremont era had a lot of nudges to other genres like sci-fi, fantasy or political thriller.
I think that the best way is to stop trying to do superheros and just go for a story that happens to have superheros.