Hi
Mith, thanks for chipping in!
Yes, why willows? Their constant motion and sound, which you mention, may be especially likely to suggest animacy. Also they grow naturally near water, and in both cases the willowy weirdness is centred around a river - the Danube in Blackwood, the Withywindle in Tolkien. Now rivers in themselves may be liminal bodies (there's always a hither shore and a thither shore), but in neither case does the river itself seem to play a specially active part.
The big difference I see is that in Blackwood, the willows are acting not on their own behalf, but as conduits for some extramundane supernatural power, whereas Old Man Willow seems very much his own tree and, for all his uncanny activity, deeply rooted in natural reality; which, I suppose, tells us a great deal abiut the difference in how the two authors viewed nature.