This match-up would be a worthy final. The Godfather: Part II is obviously going to win - arguably deservedly so - but I'd wager a portion of the people voting for it won't have seen Dr. Strangelove (or: How I Learned to Stop Worrying and Love the Bomb).
Coppola and Kubrick are two god tier directors. They're up there with Hitchcock. Even Spielberg isn't of that tier, but he'd certainly help his case if he'd stop making shit like Chore Horse. They're directors that film aficionados talk about with hushed voices and slight erections.
The Godfather: Part II is on the list of films which are better than their predecessors. While I think some on that list - Aliens, Toy Story 2 - are bullshit, GP2 (as we'll call it from here) is better than The Godfather, and The Godfather is fucking amazing. It's more intelligent, it's more compelling and it's got this ingenious branching narrative. It's like Memento only much, much better.
Dr. Strangelove requires a basic knowledge of the Cold War to understand. I was born in 1992, two years after it ended. Fortunately, I did A-Level History and they never shit the fuck up about the Cold War in degree level Politics. Therefore, I thought Dr. Strangelove was hilarious. You've gotta love Peter Sellers doing an involuntary Nazi salute, regardless of your perspective. This is how you do farce - you do it big and you do it without apologies. Kubrick's best. Fuck The Shining and fuck 2001.