FRYEAN MYTHOS: *adventure*
CAMPBELLIAN FUNCTION: *metaphysical, psychological, sociological*
These two direct-to-video cartoon-movies were the first two team-ups of Superman and Batman produced by the awkwardly titled production group, "DC Universe Animated Original Movies." Both are derived from DC comic books that I have not read.
The PUBLIC ENEMIES of the title are, in fact, the "World's Finest" team themselves. Whereas Silver Age comics showed Superman and Batman as clean-cut, well-adjusted types, later incarnations favor the idea that they're friends that constantly rag on each other. The script for ENEMIES does this passably well, though often the humorous byplay is lain on with a trowel. Just as intrusive-- as shown by the still above-- is director Sam Liu's visual trope of showing various characters with jagged shadows on their faces, regardless of light-sources. Perhaps this schtick was in the original comics-work.
In Superman comics, the hero's perpetual enemy Lex Luthor maneuvered himself into the role of the U.S. President, which became a long-running headache for the Man of Steel. ENEMIES starts with Luthor in the presidential office and ends with him leaving it, presumably because such long-term plotlines proved problematic in DTV productions. Luthor, despite running on a law-and-order platform that excoriates superhero vigilantism, has somehow improved the economy enough that even a few superheroes, such as Captain Atom and Power Girl, have pledged him their allegiance. However, Luthor's regime is marked by a catastrophe, in which a titanic kryptonite meteor is on a collision course with Earth. Yet, despite this danger, Luthor's priority is still all about getting rid of Superman. After framing the hero for murder, the pernicious president places a bounty on Superman's head, so that both real heroes and long-time villains are after him. Batman joins his buddy in a running battle with Luthor's forces, while trying to dope out a means of annihilating the killer asteroid.
The action-scenes are competently done, with the highlight being Batman's combat with a grotty looking Solomon Grundy. There are assorted re-designs, with a really bad one for Power Girl, and a total reworking of classic Superman villain Toyman, who becomes a precocious thirteen-year-old genius. (Definitely an improvement over the worthless version seen in Bruce Timm's SUPERMAN teleseries.)
SUPERMAN/BATMAN: APOCALYPSE is a comparative improvement, being directed by Lauren Montgomery with a greater emphasis on splashy, hard-hitting action-scenes. In this case the inciting storyline was DC Comics's introduction of its fourth major iteration of the "Supergirl" character, so in essence the friendship of Superman and Batman takes a back seat to the new heroine, though there's enough interplay that I would consider all three of them central characters, while others, like Wonder Woman and Big Barda, play supporting roles.
In this iteration, Superman's cousin Kara Zor-El comes to Earth in a rocket sent many years ago by her parents before the explosion of Krypton. Her parents apparently gave her no advice about how to keep a low profile and learn about Earth's customs quietly, for she panics in the unfamiliar environment and rips up big hunks of real estate before the World's Finest Team subdues her. It's not clear why Kara is such a handful. She is an adolescent with hormone problems, and she saw her parents die before she was rocketed from her homeworld, but the script doesn't quite succeed in making her a rounded character. Because she seems so fractious, Wonder Woman shows up and invites the Kryptonian heroine to come to Paradise Island and train herself. However, Supergirl isn't there very long before the forces of Superman's old foe Darkseid come looking for her.
Lacking a viable way to reach the the hellish world of Apokolips-- which is how the comics spelled the name of Darkseid's homeworld-- Superman, Batman, and Wonder Woman appeal to a former native of that world, Big Barda. In order to keep things simple, the DTV prunes away the more complicated aspects of the comics-character's backstory, so that she's just a super-tough denizen of Darkseid's world, who came to Earth to get away from her tyrannical master. However, she joins the rescue team without any real conflict.
Almost as soon as Supergirl arrives on Apokolips, Darkseid seems to bend her to his will with ridiculous ease. In the 2000s, it was almost de rigeur for every major comics-character to manifest a "dark side," and thus Supergirl turns evil, as signified by her donning an outfit worthy of an exotic dancer. (Darkseid's motivations might be more comprehensible if he wanted to seduce the super-nymphet, but he only seems to want her to be the leader of his shock troops, "the Female Furies," and doesn't even seem all that interested in messing with Superman's mind.)
So Superman fights his cousin to restore her sanity, while the other heroes run around creating as much chaos as possible on an already chaotic world. The subtler aspects of Jack Kirby's NEW GODS opus are dropped in favor of showing the Apokolipians (?) as one-dimensional devils. The script does have one tantalizing myth-reference, when Darkseid tells his minions to fetch him "the girl who fell from the sky," which puts him in the ballpark of Satan, seeking to suborn one of God's angels. But that's as far as the DTV is willing to explore metaphysical myths. Even after the Girl of Steel is returned to Earth, Darkseid drops his Satanic deceptions and shows up on Earth to duke it out with both of the Kryptonian cousins, as if he were one of Jack Kirby's more muscle-bound menaces.
Still, there are a lot of fights, with dozens of Earth-Amazons and Female Furies, so there's that.