hah, you could not have picked two preamps that are more different than those!
I do not have direct experience with either of these, but the W4S STP looks like it is going to be very much like a passive preamp, but with gain applied to the voltage so that it can drive the demanding impedance of amps. This means that the STP is going to be the most transparent to the incoming sound waveforms.
The PS Audio BHK, on the other hand, has a 12AU7 tube gain stage and a Class A discrete output stage. These two stages are going to soften the "square wave" nature of the waveforms coming from the DAC. Since your PWD DAC already has a Class A output stage (and it is written that this DAC will have a slight high-frequency rolloff), pairing with the BHK might put too much of a "laid back" character on the sound (losing even more high frequency detail and clarity/punch).
I experimented for a little while with Class D amps, but discarded them when I figured out that they just did not have enough current to drive certain speakers. I don’t know your synergy, but my experience with Class D seemed like a very nice tube amp. It had a nice full midrange, but lost bass/midbass punch and high frequency excitement.
Not knowing your system or how things sound, I would probably pick the STP with your combination of equipment so that I could keep the most amount of resolution of the sound.