I haven’t read the new Batman yet but I have seen a bunch of people doing the whole “SEE Zack Snyder, that’s how you make a Superman/Batman collaboration” on social media, which doesn’t bode well.
I did read the first Priest Justice League book. It’s really just a teaser/setup issue, and not much to judge from, but it’s a promising start. I had thought from the premise that Batman screws up and it’s somewhat about how he’s only human, but it seems clear from reading the actual book that he’s being manipulated somehow. We’ll see. The art, however, is not up to the standards of post-Rebirth DC, even failing to achieve basic stuff like making the characters look the same from panel to panel. The book ships twice monthly so the artist will rotate, so I’m not worried about it. Still, it’s an auspicious start in the art department.