In a passive biamp arrangement employing identical amplifiers, whether vertically or horizontally, any given frequency component of the input signal to the amplifiers will be subject to essentially the same gain as if only one of those amplifiers was being used full-range. Therefore there will be essentially no difference in the volume control settings that are used in the biamp and single-amp configurations. (I say "essentially" because there are some subtle effects that might result in extremely small differences, such as the very slight volume loss that can result from splitting the preamp's output signals, depending on the impedances that are involved).
MAXIMUM volume capability, before clipping occurs, may increase SLIGHTLY in the passive biamp configuration, to the extent that the output voltage swing capability of the amplifiers increases as a result of the fact that each amp would no longer have to supply current and power across the full frequency range. Or (less commonly) if the maximum volume capability of the particular combination of amp and speaker is limited by the current capability of the amp, rather than by voltage swing.
The main benefit, if any, would be with respect to sound quality.