After trying basically the same formula, but more violent, and a five year hiatus filmmakers went a different way for the third installment. Instead of John McClane being trapped in a building of some kind, he's trapped in New York City, which can become kind of claustrophobic when travel is inhibited by a terror attack.
This is also the first time we get to see John in his own city, so the fish out of water theme has pretty much been abandoned. Instead, the plot leans on John's street smarts and knowledge of the city more than anything else, as he tracks down a terrorist who set off a bomb in a downtown department store and planted a bomb in an unidentified school somewhere in the city.
While John has had a sort of sidekick in the past two films, they've most only helped him out with information or talked to him on the radio. This time he gets a literal sidekick in Zeus (Samuel L. Jackson), who is with him through most of the run time, and he acts as the sort of fish out of water this time, asking all the dumb questions so the audience can get some exposition.
The plot of a villain sending the hero on a wild goose chase, forcing him to check in at various payphones around the city (remember those?) might seem really familiar—that's because the same thing happened in the original Dirty Harry (1971). Additionally, this entry feels different that the first two film (it's summer time, we're forced to believe John went from the NYPD in the first one, to the LAPD in the second, and back to the NYPD, as if he's transferring schools) because it wasn't originally conceived as a Die Hard movie.
According to moviehole.net, a script called "Simon Says" by Johnathan Hensleigh was originally written in the early '90s on spec as a vehicle for Brandon Lee, who was, at the time, one of the most promising young action stars in Hollywood after starring in Rapid Fire, a low-budget action flick that didn't do well with critics but was received quite positively at the box office.
Tragically, Lee, the son of martial arts and film legend Brandon Lee, was killed on-set while performing a stunt involving a firearm during filming for The Crow (1993).
The "Simon Says" script was back-burnered until it found its way to director John McTiernan, director of the original Die Hard, who thought it was perfect for a Die Hard sequel (McTiernan didn't direct the first sequel because of clashes with producer Joel Silver) and got Willis on board.