I've heard some people say the bass is the hardest to drive and others say the tweeters are the hardest to drive.
Tweeters can be a difficult impedance load on an amp, as frequency goes up. Woofers require a lot of juice and can deplete the reserve power an amp has during dynamic low frequency passages.
An example of horizontal bi-amping would be to run a tube amp on the highs and mids, and a solid state amp on the lows. You get the bloom of tubes on the mids and highs, and the control and tight bottom end of solid state on the woofers.
An example of vertical bi-amping would be to run 2 identical stereo amps, but one amp per speaker. You need to split the signal from your source so you have 2 left signals feeding the dual inputs of the left amp, and split the right so you have 2 right signals feeding the right amp.
Then you have one half of the left amp powering the mids and tweeters, the other half powering the woofers.
Ditto for the right.
The benefit is with 2 amps, you have 2 power supplies, and capacitor banks (in most cases, 2 output transformers).
This way you have one amp per woofer section, instead of 2 woofer sections pounding away at one amp.
So you have twice the power, you split the difficulty of driving 2 woofer banks on one amp, and your amps are therfore less strained, and you have more headroom. Therefore distortion will go down.
I'm not sure in your case of a multichannel amp, that there will be as much benefit, due to the topology, and how much sharing of power supply and output devices there is.
Cheers