I can't speak to the intrinsic sonic characters of the Sphinx or Cronus Magnum. But given the impedance curve of the LS50, shown in the first figure here, the interaction of the speaker's impedance variation as a function of frequency with the higher output impedance of a tube amp, relative to the negligibly small output impedance of the Sphinx and nearly all other solid state amps, will alter the sound in predictable directions. Specifically, a tube amp will provide greater emphasis to frequencies at and around speaker impedance peaks (especially in the mid-range in this case), and lesser emphasis to frequencies at and around impedance troughs (especially in the mid-bass region in this case).
Those differences will probably be more pronounced connecting to the Magnum's 8 ohm taps than connecting to the 4 ohms taps, since the 8 ohm tap of a tube amp will have a higher output impedance than the 4 ohm tap. Which tap will be subjectively preferable, though, is of course not predictable, and you should try both if you purchase that or any other tube amp having multiple taps.
Also, keep in mind that you will be able to alter and tailor the sound of the Magnum significantly by substituting tubes of different makes and vintages.
Happy Thanksgiving to you and yours as well. Best regards,
-- Al