Vertical bi-amplification will work "better" if you have speakers that are a benign load on the higher frequencies and you have an abundance of power in both channels. Since the highs are relatively "coasting" in terms of power draw, the "excess" power that the supply is capable of is now available as reserve to help feed and control the much more demanding woofers. However, i must point out that this is NOT true if the amp that you are running is of true "dual mono" design since each channel has its own dedicated transformer and filter caps. As such, the supply is not being "shared" so one channel could not draw from the other. This method is more convenient than it is anything else, as it allows the amp to be placed closer to the speakers should one desire to do so.
If you have speakers that are reactive on top and multiple and / or low impedance woofers down low, each section of the speaker is pulling equally hard on the power supply. In this instance, horizontal bi-amping may provide greater benefits as you have a dedicated power supply that can cope with the demands of each frequency range on their own. This minimizes sagging of the supply for both frequency ranges simultaniously and presents a more stable stereo image. This is not to mention that this can result in less clipping being seen by the high freq drivers, which is a good thing in terms of reliability. I say this because the woofers would no longer have the capabilities to starve the power supply feeding the mids and tweeters, thus assuring them of always having adequate power to reproduce the signal.
If you gain a drastic amount of channel separation by vertically biamping, something is wrong with the design of your power amp. I say this because horizontal bi-amping is theoretically the same as running a single amp in normal stereo mode. The benefit is that you now have a dedicated power supply to each frequency range rather than to each channel. If you can hear a very noticeable difference in channel seperation using vertical over horizontal, your amps are simply poorly designed, lack channel seperation and are high in crosstalk between channels. If you are able to obtain excellent channel separation and imaging in stereo mode with one of these amps, you should be able to do the same with two of them in horizontal mode.
Obviously, the one drawback to vertical bi-amping is that you obviously need two identical amps to do this. One can horizontally bi-amp with two different amps, so long as their gain is relatively matched.
Obviously, the ultimate set-up would be to bi or tri-amp using monoblocks. This allows dedicated power supplies for not only each channel, but for each frequency range used. Channel separation and dynamic headroom are no longer part of the equation as you should have achieved the best possible in such a situation. That is, if the amps were selected so as to easily provide enough power under any conditions to each of the drivers it is connected to. It is possible to use a dedicated amp for each driver and still starve the driver IF the amp was too small to start off with to achieve the desired listening level. Sean
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