I would say the spiritual successor is more Samurai Champloo given that it was created and directed by the same guy. Runs many of the same tropes and themes, similar general plot structure. And even repeats and references specific epsiodes. Even Space Dandy takes the same base concept and just turns it into an absurdist parody mapped to a more extreme space opera setting.
But I haven’t seen Wolf’s Rain. Not a big anime guy. Just a big Shinichiro Wantanabe guy.