I listened again to some of this stuff (for instance the recordings with Vaughan) and one thing I find interesting with Hammer is that his touch on the Fender Rhodes is more expressive than on acoustic piano, where he sometimes sounds a bit cold. (Like Ahmad Jamal, although his style is completely different)
In contrast, Hammer's Rhodes playing and touch is among the more personal and captivating (in my opinion, at least).
There are other jazz players who have a very personal touch and style on the instrument (Chick Corea and Cedar Walton, to name two), but Hammer stands out as the only player I can think of who sounds *better* on Rhodes than piano in a "jazz" (rather than "fusion") context.