National Review's Armond White liked the movie, to the point of writing that "Snyder's thrillingly intelligent use of interior conflict and political antagonism vastly outclasses Christopher Nolan's Batman trilogy: Batman Begins, The Dark Knight, and The Dark Knight Rises -- all noxious -- which were bellwethers of our culture's decline". Alex Abad-Santos on Vox has a piece on Batman's views on altruism, and how he actually hypocritically doesn't "care about people as much as he said" he does. Abad-Santos's piece is full of spoilers, but I guess you should have seen the movie to fully appreciate it, and I didn't yet.
Abraham Riesman has a superb piece on all the confrontations between Batman and Superman in the past here.
The first "Batman vs Superman" scene I can remember is from a beloved graphic novel of my childhood, "Batman: the Dark Knight Returns" by Frank Miller. There, Batman is painted as a grumpy reactionary who revolts against a government which, muddied with incompetence, is waging a war against the Soviet Union. Superman, on the other hand, is a happy warrior in the service of the US government. A theme of the comic book, if I remember correctly, is Batman's being fed up with political correctness and the lack of respect for individuality (there are plenty of weirder things too: for example it takes nothing for Batman to turn a gang of criminals into an army of idealists).
My sense was most of the time that Superman was a more of an icon sympathetic to what we may call "the establishment," a defender of a status quo that he sees as benevolent, whereas Batman was instead more of an individualist (hard to say "an outsider" given the apparently endless resources available to Mr Wayne). After all, Batman becomes Batman reacting to what he sees as the injustice in this world and the ineffectiveness of government in dealing with it. Superman is Superman because he's born this way, and wants to put his power to the service of community.
But apparently in the new movie (see trailer here) one theme is the fact Superman is criticised with a protectionist and "nativist" slogan: Americans belong to Americans, and Earth to humans. Is Superman supposed to symbolise all what's good with immigration, and the fact that attracting talents is actually good for a country?