Bi-amping offers more advantages than just an additional power supply. Vertical bi-amping can offer the same benefits of monoblocks, plus the benefits of bi-amping. Bi-amping reduces the responsibility of each channel, and can offer a lot of flexibility for using active or passive crossovers. Separate amps on each channel reduces crosstalk.
I’m currently running tube monoblocks on the mids and tweeters, and a solid state amp on the woofers in a horizontal bi-amp configuration. I still use the passive crossovers on the speakers, but have the option of adding an active high pass filter for limiting the bass into the amps that drive the mids and tweeters.
With good equipment and a decent system, you should definitely hear a difference. Bi-amping with something like a modest AV receiver is less likely to offer much improvement.