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No need to wait for Superman-Batman to tackle this question! Here's one answer from "The Super-Batman!", published in World's Finest, #77, in 1955 and reprinted now in the World's Finest Archive, vol. 1.
The Grand Comics Database doesn't credit the script to anyone, but the pencils are by Curt Swan.
The action begins with Superman tracking a scientist with bad hair and an elaborate ray of some sort—what could go wrong?

As the man in the green suit has his best moment EVER shoving Superman around, Batman steps in front of the superfying ray the scientist wanted to shine on himself. Oh, the irony!
Despite explaining what's happened for the benefit of the readers at home, Superman does a Lois out the window.

This new situation requires some adjustments.

In the same way that toddlers try to comfort someone else by bringing their own favorite toy, Batman tries to cheer up Superman by giving him a snazzy convertible and his very own cave. The look on Superman's face suggests he might think that Batman is just showing off.
Batman has some difficulty himself adjusting to his new powers, such as flying so fast that Robin's costume changes colors. (Scientists call this "greenshift.") Somehow, because Batman can fly, he's no longer light on his feet.

I'm leaving out an entire subplot in which Lois Lane becomes suspicious because Superman is driving around in a car and not saving her in the usual way. During that time, Batman ostentatiously flies around the city and moves an orphanage while Superman does the deductive work to figure out what really happened. Apparently their intellects got switched, too.

Robin gets to fly with everybody!

Yes, there's something Batman can't handle: being super!
And for folks who want a souvenir to take home, an icon:

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Date: 2009-12-09 04:39 am (UTC)--LBD "Nytetrayn"
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Date: 2009-12-09 09:17 am (UTC)This was Silver Age Superman level powers, wasn't it?
The fact that the door wasn't vaporized PROVES Batman was only using a fraction of his strength.