As the title suggests, I'm going to discuss, the big two, the most recognized (though not the most popular, Marvel has those) comic book characters in the world.

I'm focusing specifically very specific graphic novels I have at home that feature Superman and Batman together, the Batman:Hush arc, the first three TP's of Superman/Batman - #1 Public Enemies, #2 Supergirl and #3 Absolute Power – Written by Jeph Loeb and The Dark Knight Returns, which was written by Frank Miller.

Frank Miller (May his homophobic, misogynistic, films, adapted from his equally homophobic, misogynistic books be laid to waste) wrote a genre changing book in the late 80's known as "The Dark Knight Returns"; it is a futuristic look at the fate of the DC universe, where Batman and Superman no longer agree to disagree (as they usually do in present times) now they really want to kill each other!
Despite my, shall we say, dislike of Frank Miller's work; "The Dark Knight Returns" is really good, it's beautifully written and the art is very (for it's time and IMO, at least) very cutting edge, that and it's unfortunate sequel - "The Dark Knight Strikes Again" - are the only Frank Miller books that will ever be on my bookshelf.

In an interview with Frank Miller I once saw, Frank Miller discussed the relationship between Superman and Batman, the way he wrote and presented it in “The Dark Knight Returns”, because of the inherent differences between the two of them could never allow their friendship to be sustained.
This makes sense on a certain level, Superman and Batman are inherently different in their approach and methodology and of course their psyche.
One could argue that Superman is the well adjusted (to a certain degree), sweet, All American tm, Hero; After all his goal (used to be at least) to defend "Truth, Justice and the American Way". He's the straight-laced, G-Man.
Batman, on the other hand, is a certified psychopath, who on occasion would seem to be no better than the certified psychopaths he fights*.
I've always found it fascinating how Superman, the arguably most non-human superhero in existence (I know the J'onn J'onzz, Scott Free and Big Barda and many other are aliens as well, but let's keep this focused on these two guys shall we) is the most Human in behaviour; I mean the only thing that ever came close to killing (and in fact did) is Doomsday. Kryptonite aside, not much can harm Superman. While Batman, the only human, not meta, superhero, wears such thick armor and a lone wolf persona** it's easy to forget sometimes that he is most vulnerable of them all. He has no "weakness"... he himself is his own weakness and he knows it... he bears many scars***.
Batman is human, the only truly human “Superhero”

Bottom line, while I agree with Mr. Miller that when it comes down to it, Superman is a Policeman, Batman is a Vigilante. They have more in common than not, because they both strive for justice for all and they complete each other in their different attitudes.

I bet you're thinking, she's going in for the feminist angle. And that's right, there is a feminist angle here, but not to do with the fact that “I'm outraged about the fact that here are two old school macho-men whose relationship with women have been iffy at best.”
I'm not outraged and they are Macho-men.
There is plenty evidence in the graphic novels I mention that Batman is an elitist chauvinist and of course Superman is superior to everyone so it's clear that he can he viewed as the Grand Patriarch.
No where is this clearer than in the third Superman/Batman TP “Absolute Power" where they are both rulers of an alternate DCU.
It's all very disturbing, since not only are they rulers they are also the enforcers of their own brand of "Justice for all".
It was nice to see the old Anarchist Oliver Quinn in his Green Arrow outfit shout-out in dissent and revolution to his old allies. And who they subsequently murder early on.

And what's very feminist about that particularly patriarchal TP?
First, the love and affection between Superman and Batman crystal clear here, it more often than not extremely rare to see unabashed affection between these two Macho Best Friends, where the closest they ever come to a hug is when one or the other is injured and they have to carry each other (most often Superman carries Batman).

Second, the leader of the rebellion against Superman and Batman's “Absolute Power” is none other that Wonder Woman (though she isn't officially called that in the TP) and she cries out in battle "For Truth! For Justice! For All of Humanity".
Not just America.
Or Mankind.

And third, in one of the best art sequences ever, we see Diana in black and gold, under a red sky stab Batman while shouting "Die Oppressor!" and thereafter Superman destroys a green eagle made by the Green Lantern's Power Ring and kills the current Green Lantern who goes by the name of Samuel (and it's very obvious, almost idiotically transparent, that Samuel is supposed to represent Uncle Sam - the classic symbol for American Militarism "Uncle Sam Wants You!" and the hardened old man points at us from the poster).
Superman cries out to the heavens while holding a dead/dying Batman, he screams "No! Bruce!" and Samuel lies dying on Liberty Island. Interestingly, the Green Lanterns are the galactic policeman.

So not only do we witness the clear love between these two men (what kind of love is debatable, but the Slash can't be ignored) which does not coincide with modern western heterosexual behaviour, but we also see the beginning of the end of their reign as dictators of this AU. With the death of Uncle Sam and the stabbing of Batman by Wonder Woman (I know very phallic) we have a metaphor to the evil of modern imperialism, which I see personified in US military aggression and globalization.

More on this subject in later posts.

Gosh this is fun! I wonder why I took such a long break from this.

Notes
* I suddenly realized the correlation between Superman and Batman to Riley Finn and Angel from "Buffy the Vampire Slayer" more on that subject at another time.

** In "Public Enemies, Part Five: State of Siege"; Lex Luthor comments, as he is surrounded by the Bat Clan, consisting of Nightwing, Robin, Huntress and Batgirl, "I've always been curious as to why Batman -- who has such a reputation for being a lone wolf -- Would surround himself with children." Emphasis Theirs.

*** In "Hush, Chapter Nine: The Assassins", there is an Interlude in the Batcave, where Alfred is tending to Bruce's wounds, this after Batman reveals his secret identity as Brose Wayne to Catwoman. Incidentally, throughout this interlude, they keep their masks on, despite the fact that Batman is shirtless and Selina is shocked at the extent of the scarring on Bruce's back;
Catwoman: Oh, God.
Batman: Something Wrong?
Catwoman: I just... Didn't expect... The scars.
Batman: Each of them carries a memory.
Catwoman: Most people opt for a photo album
Batman: *thought* I am not... most people */thought* (no, shit)
Emphasis theirs, parenthesis mine.