I submit that Tolkien's dragons are especially like cats; much more so than the usual dragons of myth and folkore. I surmise that this illustrates not only Tolkien's dislike of cats but also a grudging respect for them and even a hidden affection.
The obvious comparison is Smaug, who stretches out on his treasure like a cat and purrs when Bilbo flatters him. The riddling conversation reveals a cat who likes to play with his prey before eating him.
Smaug is un-cat-like in that he is bold and fearless. He is like an armoured cat that lives on an island with no dogs and no rival cats.
The true dragon-cat of Tolkien's stories is of course my namesake, Chrysophylax Dives, a dragon who is not over-bold. Unfortunately, as few on the plaza have read Farmer Giles of Ham there is little point exploring this comparison further.