Is there some speaker performance or design spec that signals when a voltage vs a current source is preferable?If the impedance of the speaker is relatively high, and does not vary greatly in magnitude over the frequency range, and does not have phase angles that are severely capacitive (i.e., extremely negative) at any frequency (especially at frequencies at which the impedance magnitude is low), and has medium to high sensitivity, chances are it would be suitable for use with either type of amplification.
To the extent that those criteria are not met, as Ralph (Atmasphere) has said in the past it can often be helpful to try to determine the intentions of the designer. For example, it can be inferred that a small two-way speaker having an impedance in the vicinity of 4 ohms in the bass region and 8 ohms at higher frequencies is probably intended for use with solid state amplification, which will augment the bass by delivering more current and power at bass frequencies than at higher frequencies, for a given output voltage. While the classic Quad ESL-57 electrostatic speaker was designed before solid state amplification existed, so it can be presumed to be suitable for use with tube amplification even though its impedance varies widely over the frequency range and is highly capacitive.
Best regards,
-- Al