It seems like most of the commenters are choosing Die Hard, which is odd because it's pretty close to an even split at the moment. Maybe it's because "everyone knows" that The Godfather is considered to be one of the "best" films ever, so if you like Die Hard better you feel obligated to defend that choice.
Myself, I'm the same. Sure, The Godfather is great and a cinematic landmark and all that, but Die Hard is just more fun, more entertaining, more rewatchable. It's one of the best action movies ever made, and I honestly think it has aged rather better than The Godfather for the modern movie audience.
When I want to just put on a movie, Die Hard is always one of the first ones I think of. The Godfather is more like a commitment, like you need to be in the right mindset and you need to be prepared for heavy emotions and deep investment. Die Hard is just all fun, all the way through, every time.