I've said it before and I'll say it again, but I liked Superman Returns.
^Luthor's plan made way more sense!
Well tbh, that fight follows loosely The Dark Knight Returns. Which is a great story. Batman's purpose was not to kill him, but to make Superman always remember that he beat him. Yes I know his motivation in BvS was to take him out, but it made for a great fight scene. You also have to remember, Batman is unstable, considering he had been fighting crime for so long.
There's no way Luthor would go head to head (battle of wills & wits) with Superman unless he had leverage over him like he did in BvS in the form of holding Martha hostage. In fact Luthor is like Sauron (Silmarillion and Akallabeth periods) where he uses subtlety and intrigue to manipulate his enemies and defeat them. He kills with charm.