The more I think about this film, especially after having watched Civil War, is that this simply was the wrong time for the concept of Batman and Superman fighting one and other. Cap and Iron Man having a falling out works because not only is there an existing relationship there, the reasons for the falling out stretches all the way back to the first Iron Man movie.
I'm not giving anything away but for both films collateral damage is the cause for the heroes to be fighting, the difference is with Iron Man and Cap there's history there already, it's powerful because you know these two are teammates and you know why they have chosen the side they have. And when they come to blows it's sad, it's not meant to just look cool, it's made to be emotional, it's meant to make you say 'Steve, Tony, please, stop fighting!'.
But BvS isn't that, it's two strangers fighting one and other. Why should we care? The simple fact remains that both characters don't know one and other, and if they don't know each other then you can't really build the tension the same way. What makes it worse is that both characters aren't ideologically that different. No contrast, no difference of opinion, just two people being tools towards one and other. This was simply the wrong time for this concept, it needed to be 2-3 films for this to really hit an emotional height. Instead, it's hollow.
