The second JLA/JSA teamup took place in Justice League of America #29-30. The first issue features probably my favorite JLA cover ever:
In the first book, we meet the super-powered beings of Earth-3:
Knockoffs of the Flash, Wonder Woman, Batman, Green Lantern and Superman respectively, but with one crucial difference. They are evil, and form the Crime Syndicate of America. In fact, on their world there are no superheroes, making it a pretty grim place indeed.
Note as well that this time DC embraces the concept of alternative versions of their flagship characters, Batman and Superman, although they still had yet to do so on Earth-2.
The Crime Syndicate members have been successful in their theft attempts so often, that they are getting careless. And when they learn that there are other Earths vibrating at a different speed from theirs, with superheroes to test their mettle, they decide it will be good training to face the heroes of Earth-1.
By no small coincidence, the JLA members available to face the Crime Syndicate their counterparts listed above, and at first it looks like we'll see straight matchups, but as it turns out, the villains have switched positions for the most part, so it's mixed matches, with the Flash facing Ultraman, Batman against Johnny Quick, Superman against Power Ring, and Green Lantern against Owlman. Not surprisingly, Wonder Woman and Superwoman did get to face each other, since it prevented two man against woman fights.
In each battle the supervillian initially does well, but the superhero responds better to the changing dynamics of the battle and wins. However, there is a trick that each of the villains plays on the hero in the end:
After being transported to Earth-3, the superheroes find that the villains have a home field advantage, and they are quickly subdued. Improbably, the villains, rather than doing the obvious (killing the Justice League members), decide to be sporting and find another earth to host the rubber match. Earth-2 is the obvious pick and so the Crime Syndicate studies it. But this alerts the JSA, who discover the JLA held captive around their conference table. Doctor Fate is able to disrupt the spell holding them with the lightning bolt shown on the cover long enough to learn of the impending invasion from Earth-3.
Gardner Fox rotated the JSA members for this issue. Making their first appearances in the Silver Age were Starman and Doctor Midnight, while Hawkman, Black Canary and Doctor Fate returned. Black Canary's continued presence highlights that DC was still uncomfortable with the idea of a GA and SA Wonder Woman.
In JLA #30, the JSA faces the Crime Syndicate. They manage to defeat the individual members, but as with the JLA, the villains have a trick up their sleeves that makes them the winner either way:
This sets up the rematch of the JLA versus the Crime Syndicate, and this time the JLA wins. They learn that the villains have set a trap if they free the JSA members, and so disable the trap before saving their friends and sealing the Crime Syndicate in a bubble.