There are many kind of walnut species with many differences between them, example: north american black walnut is way more dense and stiff than french walnut, that's why europeans don't use it for fretboards for musical instruments, ebony in that case is a more obvious choice. Walnut, depending on its specie, can also bring medium, medium high frequencies, koto and ebony are definitely in the high frequencies. Ebony is of course way more direct, that's why many fretless bassists love it: the "mwah" sound jumps out literaly.
Walnut is used to "color" the sound a bit with more mid frequencies, used for top's instruments bodies, backs or sides on acoustic guitars. It can be very heavy though, as ebony.
So I'd say it really depends on the specie used, still... I think it has more dwell and less dynamics response than koto or ebony. Obviously stiffer than Limba or Ayous, that's why walnut suits blockers.
To me all in all, it's an intermediate wood between the fast and stiff ones Ebony and Koto, and the more softer ones Limba and Ayous.
