The "Action/Thriller" movie really, really degenerated during the 1980's (as did most other aspects of American culture). Guys like Eastwood and Bronson may not have been great actors, but they often displayed a naturalistic charisma that usually carried the day in the movies they appeared in during the 1960's and 1970's. And the movies they appeared may not have been particularly realistic but compared to the stuff that guys like Chuck Norris and Stallone and Van Damme (and others) churned out during the 1980's, they qualified as gritty documentaries.
"Die Hard" is arguably the best of the 1980's lot, probably because its main leads were Bruce Willis, Bonnie Bedelia, and Alan Rickman. I'm not a big fan of Bruce Willis (as a side note, when he was younger, he supposedly hung out a lot in the town where I went to high school, and I've heard that he did a ton of cocaine-oriented "partying"), but he's at least a competent actor, and seems to have that naturalistic charisma that made Eastwood, Bronson, and Steve McQueen such popular figures. In "Die Hard", he plays a NY cop hoping to spend time with his estranged wife (Bedelia). A group of terrorists (who turn out to be nothing more than thieves; it was beyond the scope of 1980's "Action" cinema to raise the troubling suggestion that some terrorists actually believe in the "justice" of their cause) invade the hotel where Willis, his wife, and the company she works for are having a big party. Very quickly, the terrorists establish themselves, and Willis single-handedly has to go up against them all.
So far as it goes, the "action" of the storyline was acceptable to me, and reasonably believable. Willis's John McClane isn't the nonsensical construct of egotistical no-talents like Stallone or Norris. Willis is able to invest the character with a certain plausibility that may have been lacking in the original conception of said character (I haven't read the novel on which the movie is based, so I don't really know what was there in the author's initial vision, or how much was added by Willis). Alan Rickman is a better actor than Willis (and most of the rest of the cast), and his terrorist is very believable, and frightening (most terrorists in 1980's "action" movies were comic book Arabs).
Unfortunately, Willis and Rickman can't carry the whole movie. Director John McTiernan was responsible for movies like "Predator", so obviously the level of this film was never going to reach all that high when it came to direction. Also, in common with way too many 1980's movies, the makers of "Die Hard" do nothing to establish characters that actually resemble real human beings. They're all pretty much unbelievable but "cute" caricatures (unless they're terrorists or bureaucrats, in which case they're monochromatic stereotypes), from the wise-cracking limo driver "Argyle" (yeah...right) to the obtuse FBI agents. Whether this is the fault of the director, the screenwriter, or the author of the original novel...or a combination of all of them...I can't really say, but there's nothing of substance here at all, outside of Willis, Rickman, and maybe Bedelia. Characters are "established" by superficial quirks. Willis and Bedelia are first seen bickering over the fact that she's using her maiden name rather than her married one. This is a plot device, and you know its' ultimately going to "end cute." Too, there's a black policeman (played by Reginald VelJohnson) who becomes friendly with Willis via their communications during the siege at the hotel. He has a dark secret in his past, but because this is a 1980's film, you know he's going to "redeem" himself at the end. The late Paul Gleason played a prick disciplinarian in "The Breakfast Club" (an 80's movie I loathe) and he plays pretty much the same part here. And Alexander Godunov, who displayed genuine acting talent in "Witness" (a movie I love), has nothing much to do here except be tall and look fiercely blond as Rickman's assistant terrorist (sadly, Godunov was an alcoholic and died young; he said of his career in cinema, which never really progressed beyond "Witness", '"Producers and directors come to me and say, 'You will play the guy who comes in with a long coat and machine gun and kills everybody in the room. And use that same expression on your face you used in Die Hard.'").
So...if you like "action-thriller" style films, "Die Hard" might work for you, if you don't expect all that much from it. It's semi-plausible, occasionally well acted, and certainly not as ridiculous overall as some. It's certainly better than anything Chuck Norris or Sly Stallone put out, but that might be damning it with faint praise.
