Die Hard has two definite phases... The initial trilogy was hard. Violence, swears & a true adult sensibility. This was a major reason for their success as it gave us a witty, human and badass hero in John McClane.
In the UK the famed catchphrase was re-dubbed "Yippi-kay-ay Kee-mo-sabe" with the violence taken out. Yet the film as a whole still worked as it was clear that censorship rather than movie-making decisions were neutering John McClane...many fans would ditch the TV version for VHS and the full effect.
Two sequels kept the R-rated goodness, with Die Hard With A Vengeance adding in Samuel L. Jackson's majestic swearing ability to boot. Yet Live Free or Die Hard changed the game, making McClane a PG-13 old man. The violence was replaced with mediocre stunts, swears with bad dialogue. It all but killed Bruce Willis as an actor, much less McClane as a bankable commodity.