I would say no, although I don't have two identical styli for the same cartridge where one has an HE and the other the SH. I do have many Shibatas and many HEs and they all make nice noises....Is Shibata a lot different from hypereliptical in terms of sound?
Having said that, Shure said that the greater front-to-back symmetry of the hyperelliptical cut gave measurably lower distortion when they compared the HE to the simpler, very Shibata-looking cut on the diamond on their M24H (which I also have).
In the real world of Bliss Shibata vs Bliss HE, there may be other differences. For example, the particular Shibata in the Bliss might have a taller contact patch (bigger contact radius) than the HE counterpart. Distortion differences aside, this wouldn't affect the sound, but would affect wear. The tradeoff would be greater sensitivity to vertical tracking angle (VTA), and without further audiophile bla bla bla, you can probably see that for the extra money, you might not be getting any immediately-obvious audible benefit.
Then too, the two diamonds might have different scanning radii, which would affect detail retrieval.
Suggestion: Email/phone TTN and ask for the two important dimensions of the two diamonds: scanning radius and contact radius. The smaller the scanning radius, the higher the frequency the diamond can trace. The bigger the contact radius, the less the wear and the greater the sensitivity to vertical tracking angle.
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