For me, rewatching, I rank them as FotR -> TTT -> RotK. I love all three, but Fellowship stands as my favourite and so on.
I think what knocks back RotK a bit is how the story breaks up. As a work of literature its much easier to manage multiple narratives from multiple characters, since it's read at the readers pace and divided by chapters. With film, though, it's a totally linear, controlled experience and narrative can suffer a bit.
Fellowship works best because it's essentially an A-to-B film. There's no divide between characters, and they journey together. All elements of the plot and flow can be told from mostly a single perspective of the Fellowship itself, and its not until the end that it breaks up.
Towers works fine since the separation of characters is minimal. Frodo, Sam, and Gollum star in one narrative, while Aragorn, Legolas, and Gimli star in another, with that narrative also including Théoden, Eowyn, and Éomer, as well as Gandalf the White.
The Merry, Pippin, and Treebeard narrative is kept relatively brief, mostly relying on dialogue and the final fight, and thus doesn't feel unnecessary.
Return of the King, though, really separates a lot of the characters, and you end up with a crazy amount of narrative. Frodo, Sam and Gollum are still doing their thing, while you must also follow Aaragon, Legolas, and Gimli, then Merry and Eowyn, also Pippin and Gandalf, Faramir and Denethor, and then Arwen and Elrond.
As a novel it works, but as a film you've got a ton of characters with their own plots, small and large, to follow while constantly switching between one and the other.
It still works and makes for a fantastic film, but it changes the pace quite dramatically and I can see why some people may have felt it dragged on, as it never really settles in one particular moment until the final battles.
