On the surface, it would appear that Batman and Superman couldn’t be more different from one another. And, if one could successfully argue that point, I would agree. But eventually, those same differences that you could argue exist between the two are in fact the same characteristics that have bonded the two fictional characters in the comics (and animated films) over the years. And, I suspect the new Superman movie, Dawn of Justice, will depict just that.
Source of Pain
Although Bruce Wayne and Clark Kent grew up in different socioeconomic circumstances, they both suffered a terrible loss in early childhood which resulted in them being raised by someone other than their biological parents. As you know, Bruce Wayne was essentially raised on the Wayne estate by Alfred after his parents were murdered in cold blood right in front of him. Clark Kent, on the other hand, was raised on a farm in rural Kansas by the Kents after being orphaned when his home planet of Krypton (including his parents) exploded.
The family tragedies that both Clark Kent and Bruce Wayne endured at a young age then went on to shape the people they became in their everyday lives, as well as the kind of superheroes that they chose to become. Perhaps the violence that Bruce Wayne/Batman witnessed as a child with respect to the death of his parents, had much to do with the rage he still exhibits; particularly when engaging with the criminal element of Gotham. Although Clark Kent/Superman never knew much violence early in life and has the capability to exercise more personal restraint, he at times can be pushed beyond his own breaking point; which is likely the result of harbored anger about his past.
Destined to Be Lonely
Like all superheroes, Batman and Superman are destined to be lonely. Such is the case when one decides to take up a lifestyle of fighting crime as a vigilante. Though they both have had close friends and romantic relationships throughout the years, in the end, they know that such relationships could never be maintained over the long haul. The reason being, with their line of work the lives of their significant others/loved ones would always be in jeopardy.
Neither superhero takes such a risk lightly as to have little to no regard for the repercussions of involving others in their quest for a life of fighting crime. As a result, both Superman and Batman have spent a great deal of time by themselves; usually by refraining from contact with those they truly care about in an effort to prevent tragedy from befalling upon them. Such a lifestyle not only creates a great deal of loneliness, but may also be one of the main reasons why the two have managed to strike up a friendship; that and they both live and die for the cause.
Life Purpose
The tragedies that befell Bruce Wayne and Clark Kent early in life undoubtedly contributed to their life purpose of becoming the Batman and Superman that we know today. As a result, they both are very much committed- mind you in their own way- to ridding society of the criminal element. For instance, although Batman is perhaps more motivated by vengeance as a result of the direct impact of violence in Gotham on his own family, he is still committed to ridding the streets of Gotham of the criminal element.
Superman is kindred to Batman in this regard. He not only fights the human criminals, but also alien life forms in an attempt to keep society a safe place. This perhaps stems from the fact that he adopted Earth as his home after the demise of Krypton. But, as you can see, both superheroes apparently feel an inherent sense of duty to combat the ills of society. Although such a task does take a toll on the both of them, it also strengthens the bond between them as few others walk a similar path as they do.