Okay, so I'm not a professional at writing or making Superman into a character but I have watched and read everything I could about him and I have even written some stories about him. This is of course not definitive but it's what I've learned about the character in the years I have been reading his comics, watching his moves and TV series'.
What I think and what I gathered is that the character can be broken down into the balance of 4 traits: Clark, Clark Kent, Kal-El and Superman. These are the following:
Clark of Smallville
This is the farmboy who grew up at the Kents in Smallville. He's, in my opinion, the original character, the man before the costume, before being an alien, before everything. This is his most human part, this is his past of where he came from, what did he learn from his parents, what kind of adventures he had when he was a teenager or a pre-teen, what plans he made to when he grew up and how he got used to his powers and abilities. This was the time when he got to know Lana Lang, when he fell in love for the first time and where he decided what he wanted to be. The TV series Smallville has shown this the most prominently, other movies usually just use it as a catalyst to the character's start, which is really what it is. Other stories, like Superman: Earth One has a huge dose of this since we don't see a bumbling/fumbling Clark Kent in Metropolis or a traditional Superman hero character. In that story he's really just Clark of Smallville in uniform.
Clark Kent of the Daily Planet
This is another part of the Superman character, one where he's awkward, fumbling and really embarrassing. Many have said that he acts like this because this is how he sees us compared to him, but I don't think so. He actually does this to make others believe that he's just too awkward to be someone like Superman. In my opinion this is the most underdeveloped and even the most useless part of the character. Writers have abandoned it for a time and I'm glad they did so. In the animated movie, Superman Unbound, we see him as Clark of the Daily Planet but he is still confident in his suit. In the animated movie, All-Star Superman we can see traces and remnants of the trait throughout. The Richard Donner directed Superman movies bare this heavily as do all sequels until Man of Steel. This trait is really rare nowadays, maybe because this is really not what Superman is, it's just a fake persona he plays, like Bruce Wayne's playboy tact.
Kal-El of Krypton
This is something that I dislike but it's really a deep rooting part of the character and it's getting a lot of attention nowadays. This is the alien part of Superman, the sci-fi part of his life. We can see this everywhere, in the animated series, Smallville, maybe most heavily in All-Star Superman. This is the part where Kal-El deals with problems and issues from outer space, where he travels the stars and meets other civilizations and helps them, if he can. This is the part where he deals with Darkseid, Mongul, Lobo and other parts of alien threats and technologies. In the past, as All-Star Superman shows, this and the Clark Kent of the Daily Planet have been the two most important parts of the character and balancing these two created the Superman of old where he went on amazing adventures but then returned to the Planet to fall over his own shoes. This equal part human/alien has been the core of the character for a long time.
Superman of Earth
In this day and age, this Superman reigns supreme. This part of his character is the member of the Justice League, his best friend is Batman, he flies all around the world helping people. Superman is the superhero part who wears the red/blue outfit and catches children who run out on the road. This is my favorite part of the character and the most important in my opinion. Unfortunately we see little of this in the actual comics, often only in the stories of other characters where Superman is only a presence or a wise voice, This trait has been almost completely abandoned in the New 52 and as of yet, in Man of Steel but it had a heavy influence in the Donner Superman movies, the Lois and Clark TV series and Superman's own animated series. This is the man who gives speeches in front of the press or the senate, this is the man who smiles to the cameras and shakes hands.
So this is my opinion at least. Over the years we have seen these four traits wary in importance within the character but a good balance is always required to make Superman a slightly more complex character. People always hate on Superman for being too simple, or too much of an idiot in red tights who can only punch things. But when they do this, we should remember that Superman himself is having all these four traits in himself to wrestle with.
Thank you for reading.