Myth
Give me your babies!!!
The problem in addition to Batman being in Supes realm is simply the mood of the movie. Superman movies are a lot more light hearted while Batman is darker. If they did decide to make the movie I'd rather have it be Batman VS Superman.
I'm thinking that Superman would branch out of Metropolis and start helping in Gothem. Supes then gets all of Batman's spotlight and it starts making him jealous. It then becomes a bit of a competition until they end up meeting each other at a robbery or something. Maybe a big name Batman baddy is involved and Supes intervines stopping the bad guys. This pushes Batman over the top and attacks Superman and Supes pretty much kicks his ass in a one sided battle. Hearing of Batman's jealousy, Lex Luther contacts Bats and makes a deal with him (obviously kryptonite is involved in the deal going to Batman). Batman and Superman get in another fight later in the movie that Batman is winning in and is about to kill Superman (with the help of that Kryptonite of course). He then learns (probably with Superman informing him in some sort of begging way) that Lex had tricked Batman into dispensing of Superman while Lex is going through with his world wide evil plans. Superman eventually convinces Batman to spare him and they team up to take Lex down. The movie concludes with Batman getting the media spotlight while Superman is satisfied with being as purely good as he is.