I'm not an audiophile, just a bass player. So the main thing for me (beyond mechanical reliability, which any 3-spacer 5751 will serve up in spades) is tightness in the bottom octave. Detail in that range may seem a strange subject, so let me liken the difference between these tubes and all others to the difference between MP3 and CD. The first time I taste-tested an MP3 file against a CD, I listened to an exposed low tuba passage. In the MP3, the pitch was reproduced faithfully, but that was all. On the CD, I could fairly hear each individual juicy flapping of the tubist's lips. Now there is no way that EQ or speakers or any other device can add what's not there. It can add emphasis to a certain frequency, sure, but not detail. Of course, as a Precision Bass player, I'm a fanatic about "grunt." It's the defining characteristic of the P-bass sound, and one of the reasons that audiences feel so good about the P-sound is (first among other things) the very vocal quality imparted to the bass by "grunt."
As I say, I'm not an audiophile, but there are two themes that recur in Joe S's FAQ that translate into terms useful to the bassist. The first is that of "palpability," and the second is of spaciousness of the soundstage. Because a note from an electric bass is composed of so many discrete elements, each of which must be reproduced with integrity, I think these two measuring sticks relate equally to the production of "grunt." However, the bass grunt test cuts more finely than these. While Joe notes its relative imprecision in hi-fi equipment (compared to the magic tubes), one of the tubes that made Joe's "short list," the Tung-Sol, entirely lacks the three-dimensionality I can hear in the four magic tubes. Of course, the "grunt" I'm so crazy about is probably not present on most recordings, so it may not be a crucial issue in hi-fi tubes, but if it is there, I think it would take these magic tubes to allow you to hear it.