There were numerous interviews before BvS' release that said BvS was as dark as it would get. Only two DC movies can be called dark and even then how dark they are is greatly exaggerated.
I also love how everyone complains about Snyder being too dark while hoping Whedon can "course correct". Whedon who is mostly known for psychologically destroying his characters because he thinks it makes them better.
And then proceeded to bungle said ideological battle.
The disagreement between Superman and Batman doesn't really play because the theatrical cut utterly fails to show Superman's side of the argument and the director's cut fails to have him articulate his problem with Batman in any convincing way. Batman has become demonstrably more violent and blood thirsty, but Superman doesn't really do anything about it aside from wrecking the Batmobile and telling him to retire without doing anything about the machine gun toting bad guys Batman was chasing. Had he captured them all without maiming, torturing or blowing them up, maybe he'd have a point. However, he doesn't do that. He just totals Batman's car, threatens him and flies off. Not exactly a very convincing way of getting your point across or a particularly Superman way of dealing with the situation either.
He doesn't do anything about them because all he knows is that they were attacked by a lunatic in a bat costume at night. The weapons can be excused as them needing something to defend themselves in a crime ridden hell hole like Gotham. The director's cut also has Clark arguing that Bruce is only going after lower income people and he even has a conversation with a family member of one of Bruce's victims.
They had heavy machine guns mounted on trucks shooting up the entire neighborhood. Are you seriously trying to say that Superman should have given the benefit of the doubt to these obviously shady characters transporting something illicit under the cover of night. Unless you are claiming that the DCEU Superman is hopelessly naive chump, this makes absolutely no sense whatsoever. Poor people being oppressed by a crazed vigilante can't afford heavy munitions, a semi-truck, and a fleet of smaller trucks to defend it--criminals do.
You caught the part where Clark made it clear that it looked like the GCPD were actually HELPING the Bat Vigilante, right? No, if you're under attack by him, you don't call the cops because you have no reason to believe they'll help.
And what crimes were they committing? Shooting back at a maniac who was trying to shoot them and run them off the road?
Evidence that what they were transporting was illegal? Plenty of rich people and corporations try to discretely import important items. An argument could be made that they were transporting some new corporate secret for LexCorp and they feared corporate sabotage and/or a sudden assault by a psychopath in a bat suit. Hence? The heavy security.
There is no evidence that Batman was even slightly heroic. He was a criminal attacking a group of people who knew to expect an attack by him. Maybe they were other criminals, or maybe they were security contractors protecting a discrete shipment. Bottom line is? They didn't start shooting up the city until the Bat showed up and started trying to murder them. THEY were not the instigators of this conflict. The Bat was.
Though much is taken, much abides; and though
We are not now that strength which in old days
Moved earth and heaven, that which we are, we are,
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.
--Lord Alfred Tennyson--
I think Batman had blown up the machine gun by the time Superman showed up. Can't remember if that happens.
Either way i's fair to say he should have apprehended them, but I think if all Superman hears is gunfire and sees Batman is involved, it's not unreasonable to think he prioritizes giving Batman his ultimatum. Those other criminals, may they be smugglers or drug dealers or worse, can and probably will be caught later. But Batman is one very capable person with a symbol behind him and who considers himself above the law.