The interface between amp and main speaker is highly complex, and the signal that is present at that point reflects not only the sonic character of the amp itself (and what precedes it), but effects that depend on the speaker as well.
Those effects include phase differences between voltage and current, which depend on the degree to which the speaker's impedance is capacitive or inductive (as opposed to purely resistive), and also back-emf (voltage produced by a driver within the speaker due to its motion continuing after the signal has stopped or changed). All of those effects are highly dependent on frequency.
Since as Xti16 indicated the sub's amplifier only senses voltage and not current, its response to those effects will be partial, and will be essentially unpredictable. Whether the sonic result of that response will be for the better or for the worse therefore figures to be system-dependent, as Raquel stated.
I assume that if the signal comes from one amp or mono amps, the sub would then retain more of the sonic characteristic of the main amplifier and less from its own internal amplifier.
More of the sonic character of the main amp -- yes.
Less of the sonic character of its own internal amp -- no. I would expect the sub's internal amp to be just about entirely in the signal path to the sub's driver whether the input is taken at line-level or speaker-level. If it is taken at speaker-level, I would expect that the incoming voltage would either have a lower gain applied to it at the front end of that signal path, or else that it would simply be divided down to a line-level amplitude and then processed identically to a line-level input.
Regards,
-- Al