It would appear this town isn't big enough for the two of them.
But what brings Clark Kent and Bruce Wayne toe-to-toe? Why can't the alien and the bat get along?
Where does Wonder Woman fit in? Who's the real bad guy? What about Aquaman?
We've scoured the latest trailer for Zack Snyder's comic epic to answer these questions and more.
If you hate your spoilers, don't proceed. Should you delight in speculation, then plunge right in.
Lex Luther is doing well
The action begins at a swanky gathering of influential types - something grand enough to bring Bruce Wayne (Ben Affleck) in from Gotham and attract the attention of the Daily Planet's reporters.
We'd say that Lex Luthor (Jesse Eisenberg) is the host - already in a seat of wealth and fame. This isn't going to be a Lex 'origin story', showing his rise to power.
Batman has been kicking butt
We witness what's apparently the first meeting between Wayne and Clark Kent (Henry Cavill) - with Kent quizzing the billionaire on the vigilante who's been "trampling" civil liberties.
This meeting might well take place midway through the action of the film, introducing Batman and his rough justice in order lend some exposition to this tension.
The world is falling apart
A front page splash of a Gotham paper hints at a world of on the brink - with funding cut to water treatment plants and issues over air safety regulations. It's shortly followed by a flood scene, that sees Superman rescue a stranded family from a rooftop.
So, this could act as the perfect setting of environmental peril that sees Aquaman (Jason Momoa) wade into proceedings.
The Joker's shadow
Speculation has bounced about the internet as to who the central villain of the piece will be - and we'd suggest that it won't be the Joker.
Bruce Wayne mentions that Gotham has a "bad history with freaks dressed like clowns", following a shot of this graffitied batsuit in a glass case - a memento rather than a new threat. Batman has already tangled with the Joker, who may still be at large, but the fight won't centre on him.
Hinted at in a previous tease, the new trailer clarifies that Wayne's frustrations with Superman stem from the city-levelling battle that ensued in Man of Steel.
Bruce Wayne doesn't think that Superman's limitless freedom to exercise justice is in keeping with the powers of the land, and he's not alone...
Trial of the century
Whether through the intervention of Batman, the manipulation of Luthor or the general unrest of society, Superman is taken to court over his actions.
Some event will see the hero, previously worshipped with giant statues, fall from grace.
Batman v Superman
Okay, so this is a given - but as the tensions amount, it looks like the two superheroes look to settle their differences in a 'trial by combat' showdown.
But other than a disagreement over the protection of civil liberties, what could bring these two cape wearers into such a climactic battle?
"Flying men? Batman in a trench coat?"
Yep - within the context of the trailer, this sequence doesn't make any sense.
When you take into consideration that the costume being worn by Batman was identified as the 'Knightmare' outfit at a recent DC exhibit, taking on soldiers wearing the Superman S insignia on their shirts, it would suggest that this isn't a 'real' sequence, but a dream section - a nightmare of Bruce Wayne.
It also explains why he's backed by flying creatures, and suggests that Wayne won't be unmasked by Superman - that it's all a clichéd dream.
The majority of the film will centre on Batman and Superman's growing distrust for each other, allowing the main villain - Lex Luthor - to go about his work quietly.
He'll be whispering in the right ears, pushing the right buttons, to bring the world to the brink without revealing his hand - until the moment is ripe...
The other bad guy
...to reveal his secret weapon.
General Zod (Michael Shannon) is apparently crucial to Luthor's plans - key to some bizarre, "devilish" experiment that will see an aspect of Zod (some toughened Krypton DNA) transferred into the huge beast, and unifier of the Justice League...
The other, other bad guy
He's the seemingly unstoppable threat that will unite Batman and Superman - the reason they put their differences aside to defend the Earth.
The third act
The scale of this threat is apparently enough to draw in Wonder Woman (Gal Gadot) - a figure neither Batman nor Superman had any awareness of.
The trio take their stand against Doomsday and his creator Luthor, and thus the Justice League is formed.