(or "Oh, Look--Batman's Got Super-Powers Again!")
These days, it's rather unromantically known as 'Superman/Batman', but 'World's Finest' has been around for a long while in one form or another; for some reason, the pairing off of Batman and Superman to fight crime together is one of the most archetypal pairings in comic book history, right up there with Green Arrow and Green Lantern, the Hulk fighting the Thing, and Wonder Man and the Beast. (Yes, it is. Yes it is! Look, just shush, you! They make an awesome team!)
When making a storytelling engine for a series that takes two well-known and popular heroes and combines them, it should come as no surprise that the resulting storytelling engine is simply a mix of the two series' engines. But it's illuminating to note exactly what elements come up as predominant in a Batman/Superman mix. Obviously, the characters remain exactly the same. Batman is always going to be Batman, and Superman is always going to be Superman (with the caveat that this is a pre-Frank Miller Batman, and as such has not yet developed the intense disdain for all other super-heroes that characterizes his interaction with the DC universe of the last two decades.) They both have a fairly similar outlook on fighting crime (again, this was back in the day when the death of Batman's parents was a reason for him to fight crime, not a constant obsession that moved him to violent rage), and hence, a similar motivation and purpose.
The primary difference shows up in the setting, and the supporting cast. While Batman does of course get Robin, the most common supporting character in 'World's Finest' is Lois Lane, intrepid reporter for the Daily Planet. Commissioner Gordon barely gets a mention every few issues or so, and then only when Superman is asking him to turn on the Bat-Signal, but Lois is in practically every story. Why? Because Lois fulfills so many valuable plot functions in a single character. Her role as a reporter can help get the main characters involved in stories, her insatiable curiousity adds plot complications, and she's also valuable as that old stand-by for adventure stories, the potential victim for the hero to rescue.
The villains, too, seem to be mostly borrowed from Superman's setting, although this is to an extent misleading; these stories were published in the mid-to-late 1950s, before editor Julius Schwartz refined the focus on Batman's setting, when Batman would frequently time-travel and fight aliens just as often as Superman would. (For that matter, this was also a period when Superman would frequently fight normal thugs and gangsters, albeit ones armed with hefty chunks of Kryptonite.) Certainly, though, by a modern fan's standards, these stories seem to involve Batman fighting Superman's villains, rather than the other way around.
Why might this be? Primarily, it's because Batman's villains pose less of a challenge to Superman than vice versa; unless he's got Kryptonite to even the odds, the Riddler isn't exactly going to terrify the Man of Steel. But Batman has the reverse problem, or so it would seem; if someone can go toe to toe with Superman, then how can Batman help?
The answer is that Superman rarely defeats his enemies through simple brute force, simply because he's got so much of it that any fight is over quickly. Instead, Superman's villains tend to be seemingly invincible, but have an Achilles' heel that he can discover through deduction, and that's an area where Batman can fit in very organically. In most of the 'World's Finest' stories, you'll spot a moment where Batman is busy thinking while Superman averts disasters caused by the villain, and comes up with a hidden weakness that Superman can then exploit. (In one of the stories, Batman is bedridden with a broken leg, and still manages to solve the case by analyzing clues that Superman and Robin return to him.)
This isn't to say that Batman fits flawlessly into these settings; in several stories, they decide to give him temporary super-powers so that he and Superman can fight super-powered foes (and each other; you can tell it's the Mort Weisinger era of Superman by the way that certain story ideas are returned to every couple of years. Weisinger, a long-time Superman editor, believed strongly that certain stories sold very well, and that on average, the entire readership of comics turned over completely every two years; hence, every two years, he felt free to repeat a good idea for a story to get the sales boost. So every two years, Batman got super-powers, and he and Superman either switched identities or fought each other.) But he does fit surprisingly well into a world of aliens, time-travel, mad scientists, and futuristic technology. In fact, Batman is a much more flexible character than he seems; his world of crime noir, pseudo-realistic technology and villains, and gritty street drama might suit him well, but he's the kind of archetypal character that you can place into unusual situations and still understand how he'll react.
In other words, Batman is always Batman, even when he is in ancient Egypt. It's something worth remembering, not just for when Batman is teaming up with Superman to fight giant energy sponges, but when he's in his own series.