In addition to being a coward (saying 'You will' after supes flies away, and not directly to his face), this batman is also a fucking hypocrite.
He's ready to destroy Superman, but somehow the Joker is still alive and kicking. This movie just makes it looks as though Batman is just jealous of Superman's powers.
I'm not sure how you get this interpretation.
There's nothing hypocritical about Batman's actions. Superman isn't a human being. He's an alien and his actions caused the death of thousands of people. With Joker, he doesn't have to worry about the entire world possibly being wiped out. That's a significant difference that changes the entire dynamic. Not to mention, there's a lot of context we're still missing.
From what we do know, Superman tells Batman to stop being Batman in one of the TV spots. To someone who is already suspicious of the guy, this would be another warning sign of someone incredibly powerful exerting his authority in a way he doesn't quite like. This is a Bruce Wayne who has been active for 20 years, and one of the trailers makes it very clear that he's already seen good men turn bad. Who knows what else he's been through, but his actions are logical and in line with the brief snippets we've come to understand of him. If something like Superman turns bad, it'll end poorly for everyone in the world. That's obviously not a risk he's willing to take.
Now whether this means he truly wants to get rid of Superman or whether Alfred convinces him that's too extreme, we don't know. It's clear Alfred believes otherwise however, and it's also pretty apparent that Superman is somehow going to convince him that he doesn't have to fear him. My guess has been that he's going to ultimately test Superman and push him to his limits, but something is obviously going to happen where Batman decides to either take a leap of faith once more, and slowly begin trusting him, or Superman is going to earn his trust completely.
I'm guessing the former. I doubt he becomes fully trusting, but Batman is likely going to change his stance and maybe see how things go due to whatever Superman does.
It's much more interesting story regardless. I don't want to see some comic version of this guy who somehow knows everything and is already trustworthy of an alien he has no idea about, and that could kill him and everyone else with ease. It's bollocks that only works in comics which hardly seem to be any barometer of good storytelling.
Extreme events can test and break our principles. There's nothing more extreme than an alien coming out of nowhere who can wipe out everything, and was already responsible for the deaths of thousands, even if indirectly, thanks to one of his homeboys showing up. The question is whether Batman ultimately breaks his or not. The answer to that is predictable, but it's still interesting to see the process.