It's a mystery, but hardly a procedural. Lots of characterization. They also break the mold every so often - a "vampire" murder, an investigation into Steampunk society, "UFO's", spy thrillers, real world "superheroes," mummy curses, haunted houses, even a zombie walk and an awesome magician murder.
The episodes are just on the edge of reasonable explanations, but are mostly real world. But yes... Castle is so very like Matt Smith's Doctor. Smart, but child-like and foolish, with a touch of dirty old man thrown in. And Beckett is a smart, capable detective. When the two of them start batting around real ideas, it's akin to the Doctor and Zoe or the Doctor and Romana.
(PS: From all the pictures I've seen, Nathan Fillion and Matt Smith get along FAMOUSLY!)