Its worth noting that back during the Golden Age and Silver Age, DC heroes pretty much had no distinct personalities. They all had a generic cookie-cutter 'hero' personality and that was pretty much it. Superman and Batman got along great because they essentially had the same personality, despite their very different backstories.Before you got a crack at them, they always got along; they were the World's Finest! Did it just not make sense to you that they would have that dynamic?
That was basically it. I figured that they had completely different views on the world. Superman was a farm boy, he was raised by nice parents and thought the world was a well-ordered place. Batman was a city kid and his parents were blown away when he was five years old. Also, Superman could do anything he wanted to. Batman had to make himself and create Batman.
What Miller did was take the differences that were already present in the text and extrapolate the distinct personalities and worldviews they'd have as a result.
Now I'm not saying that the only way to portray that relationship is the way Miller portrayed it. But give the man props for taking what was, at the time, a pretty refreshing approach to superhero inter-relationships and personalities.