There are several of these stories in the Batman canon, including World's Finest #87 and #95. The temptation to give Batman the powers of his buddy Superman was obviously hard to resist. I will say that although this is a terrific story (drawn by Sprang), Moldoff's cover leaves something to be desired. The background is dull and uninspired, and Batman looks like he's about to do a face-plant in front of his enemies instead of swooping in on them.
In the story, Batman feels an odd compulsion to go out without the assistance of Robin one evening. As he flies in the Batplane, he is suddenly transported into another dimension, where he meets his alien counterpart: Who explains that he was inspired to become the Batman of his world by viewing the Caped Crusader's adventures on Earth. Of course, this is very familiar territory, with at least two future Batman-inspired fighters (Bron Wayne and Brane Taylor), not to mention the foreign clones like the Knight and the Squire from England, the Legionary from Italy, and the Gaucho from Argentina.
We learn that the science on Zur-en-Arrh is far advanced over that of Earth: The alien Batman uses this device to stall the engines of his quarry. However, he now faces a problem beyond his abilities and science: An invasion force. Fortunately Earth's Batman has super-powers on Zur-en-Arrh: At first Batman's super powers are enough to handle the aliens, but then: Eventually the Batman of Zur-en-Arrh realizes that his Bat-radia will prevent the aliens from turning invisible, and his Terran counterpart is able to wipe up the invasion force: Batman returns to Earth. Was it all a dream? Nope, because in his hand is the Bat-radia, which his buddy from Zur-en-Arrh gave him before sending him homeward.
Comments: Definitely a fun and entertaining story, livened a bit by Sprang's gorgeous artwork. This story was referenced in the recent Grant Morrison run in Batman, although as far as I can figure out, the words "Zur-en-Arrh" were used as a trigger phrase.