^ Bruce and Clark shouldn't be at odds unless there's a reason for them to be, which is why I think you need an external catalyst, and the simplest way to provide that catalyst is through the use of a villain. I personally think that villain should be someone from Batman's rogues gallery, such as Joker, Scarecrow, Mad Hatter, or The Riddler, as they can also provide the catalyst for Bruce and Clark realizing they're on the same side and working together after initially being at odds.
in the comics there was a distrust that Batman has with Kal-el
Bruce can't believe or trust that someone with so much power, so much ability can perfect and all good. Batman in the comics and most recently shown in the DC animated movies, ect. he has a fail safe to stop all member of the league in case they go rouge or "evil".
Batman is from Gotham when no one is all "good", no one. not even himself. so for him to see this Alien come to earth and swear he is all good, in this universe I'm sure Bruce would have seen the news, a being with great abilites bringing such threats to the earth, the devastation that metropolis went though. Batman in this universe would not trust Superman at all.
so by "fighting" the man of steel in some kind of make shift armor, he can test the views of Superman, will superman spare Batman or kill him, All Kal-el would have to do is not kill Bruce and they will have an understanding. Bruce will see he is something of hope, truth and justice.
they are the same qualities Batman holds, only one is will to break bones, beat down, get their hands dirty.
it's batman/superman 101 really.
and i think that could be a great starting point.
EDIT AFTER THOUGHT: i also think having it be the two character figure it out is more character based and character driven for the story. having a villain be a catalyst seems too showy and too "marvel" (not hating on marvel i just think the two should aim for different ways about their franchises)
and i know we have Snyder here making this, he seems to be showy and less into complete character driven pieces/scenes but i think, in my opinion, having Batman and Kal-el sort one another out would not only benefit well for a critics standpoint but the audience will be able to have a clear sight into who these heroes are, what they stand for, and what they aim to achieve.