JM DeMatteis was, by 1995, a celebrated Batman writer and known as the guy who took Spider-Man to a very, very dark place in Kraven’s Last Hunt. As such, he is the perfect guy to write a team-up.
The story starts with Peter Parker having a nightmare about Joker (why does he always have to be the villain in these Marvel/DC crossovers?) killing Bruce Wayne’s parent, and then we see Bruce Wayne dreaming about the burglar who shot Ben Parker.
From there, the imprisoned Carnage and Joker are experimented on by a scientist trying to “cure evil” and, of course, it goes wrong, the two escape, and team up (at first)…
…Until they realize they have different philosophies about mass homicide.
Then, each are hunted by the other’s nemesis until the big finale where the heroes win, together.
Although this is mostly by the numbers, it’s interesting that there aren’t a bunch of cameos by other characters–that’s usually the M.O. for these kinds of crossovers.