Wow the business end here. Better put some effort into the working out.
Story : T2 is a much better story. Die Hard nails it in its simplicity, but T2 was just better.
Action : Brucie with hair, barefoot, starting off with not much and bossing the show. T2 was highly stylised while DH was raw action.
Characters : much better development of characters in DH.
Cinematography : T2. A Greenberg masterpiece.
Direction : This sent Cameron to the upper echelon while McTiernen after so much promise is now probably only Directing his Lunch. A much bigger director than Cameron in '88, he hasn't Directed a film in a decade. Although different Films, I'd give it to Cameron for the sheer scale of his vision.
I'd go for T2, because of the innovation of the Special Effects, the cultural significance of its impact into mainstream conciousness, and because it has slightly better catchphrases.