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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: 2009-12-08 04:16 am (UTC)no subject
Date: 2009-12-08 04:19 am (UTC)no subject
Date: 2009-12-08 04:20 am (UTC)no subject
Date: 2009-12-08 05:00 am (UTC)no subject
Date: 2009-12-08 06:20 am (UTC)no subject
Date: 2009-12-08 08:14 am (UTC)no subject
Date: 2009-12-08 04:19 am (UTC)Sure in that later story Bruce turned into a power-hungry maniac bending the world to his will, but I kind of prefer him just being a doofus who keeps breaking everything. Seriously, Bruce, how much strength do you usually use to open a door if you're taking the thing off its hinges?
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Date: 2009-12-08 04:55 am (UTC)no subject
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.
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Date: 2009-12-08 09:34 am (UTC)no subject
Date: 2009-12-08 10:31 am (UTC)Also - watch it, Bats! You're wrecking the place, and Alfred has to clean up after you! Don't make extra work for the loyal servant, or he won't stay loyal much longer.
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Date: 2009-12-08 10:58 am (UTC)"Say, now that you're a powerless scmuck, you need someplace to change into your civvies. Didn't you used to be able to tunnel through walls? Much like this? Haha, now if you'll excuse me, there's an orphanage that needs relocating."
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Date: 2009-12-08 12:52 pm (UTC)no subject
Date: 2009-12-08 01:36 pm (UTC)no subject
Date: 2009-12-08 06:43 pm (UTC)