Bi Amping: highs and lows or a seperate amp for the left and right.

Two identical stereo amps run in a vertical bi-amp configuration (one amp on each speaker) have similar advantages as monoblocks...physical separation, no crosstalk, and a dedicated power supply for each speaker. Plus, you can run the tweeters or mids/tweeters from a channel that doesn’t have the burden of driving heavier woofers, which has some benefit too.

Two non-identical amps in a horizontal bi-amp configuration can allow you to do something like dedicating a sweet sounding smaller amp (like a tube amp) on the tweeters or mids/tweeters, and a ballsy solid stage on the bottom. You just need to be able to match levels of the amps.

You can also do a hybrid bi-amp configuration by using monoblocks on the top, and a stereo SS on the bottom.

There are pros and cons to each approach, and every situation is a bit different, so there’s really no one size fits all scenario. In my case, I had two Dynaco/VTA 70 tube amps that are wonderful in the mids and highs, but not quite as authoritative on the bottom end, so I added an integrated SS amp to drive the woofers below 80hz.

"Plus, you can run the tweeters or mids/tweeters from a channel that doesn’t have the burden of driving heavier woofers, which has some benefit too." Not in vertical. There, the amp's ONE channel is burdened, and typical stereo amps share power supply. THAT would be (to me) the only reason to run HORIZONTAL, keep the heavy lifting in one amp, and easy peasy for mid/high with the other stereo amp.

But as you stated, differences likely minor. And vertical already sees the load on each amp 'halfed', plus crosstalk/separation, etc. Would be sweet to be able to physcially place each stereo amp near the speaker to reduce long speaker wires (and run low voltage signal lines for the distance). Or? 
 

With a vertical stereo bi-amp configuration, there’s still the benefit of the tweeter (and mid) running on a different circuit than the woofer. Even if the power supply is shared by two channels, each channel sees a different circuit load (assuming passive crossover), so the low frequencies aren’t traveling on the tweeter circuit due to the high capacitance from the crossover, so less IM distortion. If the crossover is active, each circuit is still separate, which is better than sharing the circuit.

Depending on other variables, high frequencies drivers are typically easier to drive than a woofer, so put less stress on the outputs and little draw from the PS, which may offer some sonic benefit.