Die Hard the original but it's neck and neck. It's like that for me with the the Bourne movies.
I like to watch Vengeance in the summer because of its setting. I do the same thing with Live Free Or Die Hard, which is a Die Hard movie through and through; it has all of the franchise hallmarks.
A Good Day to Die Hard is one of the worst movies I've ever seen. The previous four entries were all adaptations, or in Vengeance's case, not originally a Die Hard screenplay. The fifth one was the only one that was written as an original Die Hard film. And coincidentally, it's the only one that ends up feeling like it's not a Die Hard film and just a throwaway, garbage action movie.