ive used the Wh1, the whammy II and the whammy IV, all work the same on bass but the newer ones sound a little more "dry" than the old one.
if you want polyphonic pitch shifting/harmonies i'd look into the new whammy 5
[url="http://www.digitech.com/en-US/products/whammy-5th-gen"]http://www.digitech.com/en-US/products/whammy-5th-gen[/url]
otherwise, i'd recommend getting a line6 M5 (or above) and setting up your own pitch shifters with an external expression pedal, you can dial in any combination of shifts/harmonies you want, and can cover the stuff from the old bass whammy too (plus you get trillions of other effects), i've had best results doing this.
all the whammy pedals ive tried track the same on bass, the only difference for the bass whammy was settings if i remember correctly.