Freaky friday style, it was done on purpose to give each other a sense of the 'other side' and they both know it will last one week.
An obvious difference is their fighting styles with superman having to always hold back so he doesn't break things, but he has no real fighting talent, whereas Bruce is used to fighting at his full potential.
Superman (Batman's body) has to deal with usual street crime and a mysterious killer attacking policemen.
Whereas Batman (Superman's body) has to prepare and fend of an attack from Doomsday
They don't have eachother's memories (Like Spider-Ock)
What would happen?