Due for release later this month, the trade paperback collection Dark Knight Over Metropolis collects two meetings of the erstwhile "World's Finest Duo" from this period. The earliest of these, and the one from which this volume's Art Adams drawn cover is taken, is "Skeeter", written by Byrne with pencils by Adams inked by Dick Giordano, from Action Comics Annual #1, which came out during Action's brief stint as a Superman team-up book. The story has Batman reluctantly calling on Superman for help when he confronts a situation he is forced to concede that he cannot handle by himself; vampires overrunning a small Louisiana town.
The core of the book is "Dark Knight Over Metropolis", three part story that ran through the trio of Superman titles cover dated June 1990. The first installment in Superman #44 is written and penciled by Jerry Ordway with inks by Dennis Janke. Part two from The Adventures of Superman #467 is written and penciled by Dan Jurgens and inked by Art Thibert. Roger Stern wrote Action Comics #654's conclusion with art by Bob McLeod and Brett Breeding. Investigating a mysterious death in his hometown of Gotham lands the Dark Knight in Superman's territory and smack dab in the middle of the Man of Steel's ongoing plotlines. In between following up leads to the case that brought him to Metropolis, Batman aids Superman in protecting Clark Kent's Daily Planet colleague Cat Grant from attacks by such second rate villains as Chiller and Shockwave (Where, you almost have to wonder, was Bolt?) when Grant is targeted for death by the organized crime outfit Intergang after daring to agree to testify against former Galaxy Communications chief and Intergang operative Morgan Edge.
Also stated to included in the collection are the issues of Action and Adventures that immediately precede the "Dark Knight Over Metropolis" story. While the events of Action #653 are a direct prelude to those issues, Adventures of Superman #466 contains only a few panels directly pertaining to the Intergang sub-plot. The issue's main story is most notable for being the debut of Hank Henshaw, who would go on to infamy as the Cyborg Superman in the post Doomsday "Reign of the Superman" epic.
The ending of "Dark Knight Over Metropolis", does contain, as the Collected Editions blog states, "...an important event in post-Crisis continuity." It also serves to wrap up a dangling plot thread dating all the way back to Superman #2. Furthermore, that aforementioned "important event" signaled the beginning of the softening of relations between DC's two top crime fighters. Eventually, the two would again become good friends and even come to have shared adventures in a communal title. However, in the post Man of Steel continuity, instead of being presented with that friendship as a predetermined fact, readers got to see it grow and evolve over time. "Dark Knight Over Metropolis" signalled the true beginning of that evolution.
I would definitely recommend that you read these stories. However, I suspect that if you're willing to do a little digging through back issue boxes you might be able to pick up the individual issues for somewhat less than the cost of the upcoming trade paperback.