If Superman wanted it always Superman but the real answer is whoever the writer wants to win
That is the ultimate truth of every superhero smackdown.
For a look at what Superman would be like if he didn't hold back check out last year's issues of Earth 2. The evil
Superman pretty much anhillates every superhero he comes across - it isn't even close - until a new Superman arrives.
Even Earth 2 Batman has the good sense not to take him on - he rips off giant-size atom's arm and beats him over the head with it. That version of Superman would wipe his ass with Batman's cape.
Part of the reason Superman gets his ass kicked by Batman in DKR is that all along he's holding back, not really wanting to fight.
Sadly, I feel like he's going to get a very undeserved ass-kicking in B v S, for the same reason.
While on one level it's neat to think that Batman, who's just a man, can take down someone who's virtually a god, we should remember that he literally had to die to do it, in DKR and only with an intense amount of cunning, and preparation. Miller scripts and draws it in such a way that we can buy it.
. In DKSA he beats up Superman without breaking a sweat, which lost me right away, aside from the general crappiness of that book.
But at the end of the day, it is the writer who is god (at least for his/her run on the particular book), which is why under John Byrne Lobo nearly killed Superman but a year or two later Supes knocked him into orbit with a single punch.