I think that the poll question would be more accurate if it were "Which one was worse - Zack Snyder's Superman vs Zack Snyder's Batman?" - the really bad aspects of those characters don't appear to have come from Cavill or Affleck.
I think that the major problems with the characters stem from the same two things:
1. Their standard hero careers happen off-screen.
For Superman, we see his early life and how we becomes Superman in Man of Steel. Then, by the time Batman V Superman comes along, he's already a big established hero and all he does in the films from there is fight against gigantic world-ending threats. It's like if we only saw Iron Man and then jumped to Infinity War (maybe with a few scenes from other films added as flashbacks). All the character-defining stuff happens out of sight.
With Batman there's an even bigger gap because we're introduced to an older Batman coming towards the end of his career. The movie is happy to show the results of big character events (like Robin's murder), but those references only go part-way towards explaining the character behaviour we're seeing on-screen. It feels like we're missing a trilogy of films that show how this Batman got from Year One to here.
2. Zack Snyder's need to do big moments.
Snyder really does know how to set up a visually striking scene. You know the ones. The trinity of DC heroes standing, ready for battle, surrounded by flames. Superman, testifying in court, suited up, a being of stupendously cosmic power answering to civil authority. Bruce Wayne, running towards the collapsing building. If you look through Batman V Superman or Justice League, you will find tons of really brilliant desktop wallpapers.
What Snyder isn't so good at is figuring out why those scenes should happen - the motivations that drive the characters to do what they're doing and the plot that moves the characters into those positions. That means a lot of both BvS and Justice League are kind of paper-thin setups for the next desktop wallpaper that needs to happen. Batman and Superman aren't doing the things that a familiar Batman or Superman might do, they're doing the things that need to happen to get them to the next big set-piece or iconic comic-book moment.
So who's worse? Since the biggest problems affect them both equally, it's a really close call. They're both too careless - a character trait that doesn't suit either, but especially doesn't suit Batman. They're both too grim and humourless - again, character traits that don't really suit either, but these ones especially don't suit Superman. In the end I think Superman is worse - the misunderstandings about his character are bigger than the ones about Batman, and would have been easier to fix. Shazam! even manages to inch the character closer to where it should have been, so Superman's own films should have done a better job than that.
