Based on Frank Miller's other work (Daredevil, Punisher, 300, etc.) and his writing on this specific comic series, I would say the narrative design intent is probably that Batman is stronger because he is willing to be ruthless and dedicated and assert himself and do whatever it takes to crush his enemies.
Superman has more potential power, but is not as "strong" as Batman and so is actually weaker and loses to the dedicated hard core strong man when they come into actual conflict.
The Dark Knight Returns is a Batman story, so of course Batman wins. This isn't about balance, this is about narrative.
Batman narratives have, for decades now, been primarily cynical, and have cynical views of power. The stance that you are willing to "do whatever it takes" includes doing things that are immoral or unethical.
Good Superman stories, however, have a different view of power - in them, Superman can operate not because he has more power, or because he can "do whatever it takes". He operates because he has empathy, and establishes and retains moral and ethical authority. We can see this isn't a good Superman story because it works on the basis of Superman having ceded his moral authority to the government. It required Superman to work on Batman's basis, not his own, so of course he loses.
I mean, if you allow that losing his home, his finances, losing Alfred to a stroke, and risking his own heart attack is "winning" for Bruce. If that's a win... well, we know Bruce is kind of screwed up anyway.
If the Dark Knight Returns was a good Superman story, when asked to take down his long-time ally, Superman would approach this differently. Clark's not a genius, but he's not an idiot - he knows Bruce is a planner. He would not simply agree to meet on a terrain Bats agrees to. He'd approach Batman in a time and place Bruce wasn't controlling, and arrange with Bruce to fake that fight, so Bruce could fake is own death and escape authorities. In doing this, Superman would be retaking the moral high ground he'd ceded to authorities, making it a win for Superman.