It's a bad comparison because they are nothing alike. Visually, their styles couldn't be any different. Kubrick was meticulous with every shot, often framing as symmetrically as possible. Nolan even recently mentioned how he awed at Kubrick's ability to find the perfect shot and have the confidence to hold on it, something Nolan has never done. Kubrick's average shot length over his career was around 10.77 seconds. Nolan's is 4.1. That's a huge difference. Nolan's never staged a single long take, while Kubrick's average take was over ten seconds. Likewise, Nolan has stated he doesn't use a shot sheet and shoots lots of coverage. Michael Caine called him a "machine gun" director. Kubrick often covered a whole scene in one shot, rarely shooting coverage, which is probably one reason why he could afford his infamous copious amounts of takes. Visually, Wes Anderson earns comparisons to Kubrick. His framing, composition and rhythm of editing is much closer in line with Kubrick's than Nolan's. Visually, Nolan and Kubrick have practically nothing in common.
Thematically, they are nothing alike, either. Both filmmakers create "difficult" films, but they are "difficult" for completely different reasons. Nolan's films are "difficult" because of structure(non-linear storytelling, twists etc) whereas, aside from The Killing, Kubrick's plots are rather basic. Kubrick's films are "difficult" because his films don't reveal much on the surface, instead forcing the audience to dig through the subtext to discover the meaning of the film. Kubrick rarely explains much, whereas Nolan's biggest criticism is his exposition and his tendency to over explain. Since many want to compare 2001 to Interstellar we can compare how the whole last act of 2001 is completely unexplained compared to Anne Hathaway giving a monologue about the possible power of love and Matthew McConaughey talking to TARS which effectively acts as a way for him to walk the audience through the non-conventional climax of Interstellar.
Continuing their differences thematically, one must look at how Nolan's films are often hopeful, showing the inherent good in mankind, whereas Kubrick's films are much more bleak and, on top of that, Kubrick often exploits the bleakness for a joke. Stanley Kubrick's The Dark Knight would have ended with those ferries blowing up.
This isn't about who's better or anything like that. I'm not trying to make a post claiming Nolan can't hold Kubrick's jock or anything like that. They just aren't similar filmmakers at all and I feel like the comparison is made because Kubrick is often called a genius and some posters feel calling Nolan "this generation's Kubrick" is a smart or cool way to say Nolan's a genius, when in fact that statement is a lot more flimsy than just saying "Nolan's a genius!"
