Ok here is what I really believe would make a great Superman/Batman movie.
I think the movie should have Lex Luthor Interacting with Bruce Wayne a lot, and also show the fact that Lex is a twisted businessman and that Superman really wants to stop him from cheating and lying himself into metropolis' top businessman (maybe even have Clark write some articles on him). But Superman should be too busy trying to fight Batman that he doesn't have time.
I think the main plot to the the movie should be that Darkseid is beginning his invasion on the planet, and Superman believes that Batman is helping him get his armies of Parademons to earth. And Batman believes it's all related to Superman because he is an alien and there's already been a Kryptonian attack on Earth and it was technically because of Superman. Behind the scenes Lex Luthor has been pulling strings, and he has convinced both Superman and Batman that they are enemies and must stop each other. All of this (except for Darkseids invasion of Earth) was part of Luthors plan to rid the Earth of Superheros.
By the end of the movie you will have two fully established Villains, an arc villain for the upcoming Justice League film (Darkseid), and Superman and Batman will have faced off and will realize that neither of them are the enemy. After the credits their will be a clip of Lex Luthor talking over the phone (or computer or any other means of long distance conversation) with some extraterrestrial being (who happens to be Braniac but some of the audience may not know this). And Luthor tells Braniac that he will help him get full control of earths internet if Braniac will help him stop Darkseid and Earths two other biggest threats, Superman and Batman. You now have another villain, and a plot for the upcoming Justice League Movie!
A lot of this was inspired by New 52 comics that I have read.
Please let me know what you guys think about this (I personally would be so happy if the movie turned out like this) and if anyone has any other ideas i'd love to see them!