Because it has a great generic villain who has no charisma or charm and even does the cliche "kill his own henchman" thing. I need to know my badguys are bad! Gruber was just too darn likeable, I wanted to have a beer with him and talk about men's fashion, not shoot him!
It masterfully contrives even the same supporting cast to return in wonderfully coincidental meetings, like the tv reporter being on the same plane as McClane's wife that just happens to be the one the terrorists take over!
It doesn't waste any time on setting things up that will be paid off down the line in satisfying ways, and gets to the shooting as fast as possible.
Thought McClane jumping off the Nakatomi building was cool? Well try having him use an ejector seat to blast hilariously straight up at the camera!
He says turns yippe kay yay into a hip catchphrase he says to nobody but himself!
It gets rid of all those pesky dynamic moving camera shots and sense of geography that McTiernan was obsessed with and gives us some good old fashioned plain cinematography.
It's just plain
better.
From best to worst:
Die Hard with a Vengeance
Die Hard
Die Hard 2
Live Free or Die Hard
The one we don't talk about
Die Hard 3 is pretty great but it's not better than 1. It really starts losing steam in the third act, and ups to the stunts to kind of a silly degree, until it reaches a totally limp conclusion. It's just not as tightly scripted as the first movie, which is a nigh perfect example of setup/payoff and special geography in an action movie. Also, I feel like it's kind of a downer how shitty McClane's life turned out in that one after the first movie was this ultimate feel good Christmas blockbuster.