The most important thing to remember about Tony Stark is that he is first and foremost an engineer. He's not some generic comic book super-scientist, he's not a theorist, and he's not an explorer. He's a man of science, but even more to the point he's a practical thinker: he sees problems and he solves them.
Tony Stark has control issues. He has trouble relating to people - one of the hallmarks of his character since all the way back in Stan's day, when he was cold and distant towards the people in his life, burdened by the terrible secret of the heart problem that was slowly killing him. He's never been one to let others in. He appears as imperturbable as his metal armor. Time and again he is pulled up short by his inability to trust other people, even his closest friends and lovers. This is pretty much the oldest Iron Man story formula in the books: Tony thinks he has the situation under control, he refuses to ask his friends for help, and things only get worse the more headstrong he becomes.
As many problems as there were with the execution - and boy were there ever problems with the execution - the core idea at the root of Civil War was a sound one. Anyone who had a problem with conceiving of Iron Man and Captain America coming to blows over the finer points of ethical behavior should just think back to the last few times Iron Man and Captain America came to blows over ethical behavior. This is right at the heart of why these characters play off each other so well: Cap is an idealist, Iron Man is a pragmatist. It's the difference between ends and means. Cap has seen too much war and too much death to ever believe that any good can come from compromising your beliefs in the name of expedience. Iron Man believes in nothing so much as his own ability to solve problems. Captain America goes through periodic crises of confidence, wherein his resolve is tested by the discrepancy between his ideals and our reality; Iron Man goes through periodic crises of distrust, wherein his failure to fully control the consequences of his actions and his inability to trust the people around him alienates friends and allies.
This is why, as fun as the movies can be, Robert Downey Jr.'s portrayal of Tony Stark is completely wrong in a few crucial aspects. Downey plays Tony Stark as if Stark were a version of himself - hyperactive, ebullient, sarcastic. He's a happy man, secure in the knowledge that he's the smartest asshole in the room, and smug enough to know that everyone else understands that fact perfectly well. In the movies Tony Stark is funny, and perhaps more importantly he's sexy. The character has a great appeal and it's not hard to understand why the immense success of the movies has influenced the character's portrayal in the comics.
The problem is that while the movies certainly do a good job of filling in a general outline of Stark's character, they miss something very important: Tony Stark takes himself very seriously, and furthermore, he's very serious about having dedicated his life to helping others. He took himself seriously before receiving a chestful of shrapnel in Vietnam, and he took himself even more seriously when he had to plug his armor into a wall socket every few hours in order to stay alive. He took himself so seriously that when he had trouble keeping his act together, when circumstances threatened to become overwhelming, he turned inward and self-medicated with alcohol. And when he did that, he lost control of everything. He's not someone who would throw a massive party in his Iron Man armor and show off for some pretty starlets. He's not a happy drunk, not at all - when he falls far enough to drink, he's a self-pitying, melancholy mess.
Movie Iron Man is a loose cannon, distrusted by the government and impossible to control. In the comics, of course, Iron Man has been cast as a humorless straight-man more-or-less since time immemorial. Tony Stark takes his responsibilities very seriously. It's important to remember that Tony Stark was a full-grown adult when he became Iron Man, with an established world view and personality. The one important thing that changed in Stark as a result of the circumstances that led to his becoming Iron Man was that he became a philanthropist, someone who dedicated his time and resources to helping others - someone who believed it was his duty to help others, because he was the only one worthy to be trusted with the secrets of his armor. Compare that to Captain America, who is defined primarily by his ability to inspire the best in others, or even Thor, who considers his duty as a hero to be a function of his inherent nobility of a warrior, and you see why Iron Man stands apart. He's a bleeding heart, but it's coming from a very weird place - born rich and privileged beyond most people's wildest dreams, when he comes to responsibility he comes to it as a kind of individual mandate. There's always something just a little bit condescending in Iron Man's tone - something inextricably WASP-y and old-money - that stands at odds with the egalitarian language utilized by Captain America or the honor code that motivates Thor. He's not motivated by anything as fancy as ideals or honor, but plain old ethical pragmatism. He sees problems and tries to solve them, because he sees himself as the most qualified person in the room when it comes to solving problems.
Which is not to say for one second that his desire to help the world is anything less than entirely sincere. The problems are that he isn't entirely selfless, and he isn't capable of identifying his own shortcomings. He ends up making the same mistakes over and over again, because while he may be one of the smartest men on the planet he's still not smart enough to recognize his own hubris.
Stan Lee always says that Iron Man, of all the original Marvel hero books, was the most popular with women. They received more fan letters from women for Iron Man than any other character. It's not hard to see why: originally, Tony Stark was drawn by Don Heck as pretty much the spitting image of Clark Gable, down to the pencil mustache on his upper lip. He wasn't a lothario by any means, but he was a grown adult who carried himself as a grown adult, albeit an extremely attractive and powerful adult, and one who also carried the strange secret of a literally wounded heart. Is there any metaphor more likely to win a young girl's fancy?
For decades Iron Man's gimmick was that Tony Stark had some kind of disability. First, he was dying of heart failure because there was shrapnel suspended near his heart. Then, after his heart was fixed, he developed a problem with alcohol, and his battle with alcohol eventually led to him losing complete control of his company, his money, the Iron Man armor, and even his life for a significant amount of time. After he regained control following that he was shot by a jealous lover and spent a year in a wheelchair, after which he was cured by an experimental surgical implant that enabled a group of villains to take control of his body - the upshot of getting free of that situation was that he was left almost entirely paralyzed and near death. He faked his death after that, a decision that (sing the chorus!) alienated his closest friends and allies for years. (And then, well, it was revealed that he had been mind-controlled by Kang since 1964 and turned into a murderer before being replaced by his teen counterpart from an alternate Earth . . . well, the less said about that the better.)
The point is that he has always been a "hard luck hero," but he was never obsessed with self-pity. He didn't mope around like Spider-Man - certainly an attractive identification figure for insecure male readers but hardly a romantic ideal for young women to lionize. (At least not initially - I know plenty of women have fictional crushes on Peter Parker, but compare the portrayal of the male protagonists in Lee & Heck's earliest Iron Man stories with Lee & Ditko's Spider-Man and you'll see a world of difference - which of those two characters do you think you most resemble, and which do you want to actually be?) He was / is attractive to women because he was vulnerable but not obsessed with his vulnerability - that his confidence is often belied by reality is perfectly besides the point. His lack of self-reflection was always the root of his greatest problem. It's been years since Tony Stark has had an actual physical disability, and in that time it's become sufficient merely to assert that Stark's greatest weakness is his poisonous self-regard.
Would people otherwise have trouble identifying with an insanely wealthy protagonist, if he weren't on some level a highly dysfunctional person? Batman is rich as Croesus and people have rarely felt that this attribute made the character less relatable. Batman is a wish-fulfillment fantasy par excellence - his money is a means by which he achieves his goal of avenging his parents and fighting crime. Iron Man, however, isn't working from any kind of primal trauma. He's actually kind of insufferable - and this is true of every Iron Man, in any medium. The character is less approachable than Batman or Spider-Man or even - I would argue - Superman, because there's something in Tony Stark's character that keeps him from ever being the purely selfless heroic ideal. He's a businessman and an engineer, a man of rationality with a supreme confidence in his own ability to fix any situation, no matter how seemingly insoluble. He's not a family man like Reed Richards and he doesn't have the family trauma of Peter Parker or Bruce Wayne (although it was explained in hindsight that his family was cold and distant, it was hardly a defining trait), so the only things that keep him grounded are his own feet of clay. His model of do-gooding is profoundly philanthropic - sincere and serious-minded, but vaguely condescending for all that.
Iron Man is unique in super-hero comics because he's a protagonist the audience is often encouraged to dislike, either obliquely or explicitly. His greatest conflicts usually involve overcoming his own highly inflated sense of importance, and dealing with the repercussions of bad decisions made in the name of utility. He will always be the "cool exec with a heart of steel," a plutocrat who has perversely dedicated himself to the betterment of mankind - but on his terms and no others.