What’s the Right Power Amp Ratio For Bi-Amping?

The question boils down to this: if you had the ability to measure power consumption of white noise (equal amplitude across the audible spectrum, not necessarily 20Hz to 20kHz, if you could do it for 50Hz to 10kHz that would be a sufficient demonstration) by the two halves of a bi-amped speaker, what would you see? 

@vinylfan62, actually, I have bi-amped, in the past (first time in 1972) and currently. It's nice that your Bedini 25/25 (I ran one for years with my old QUAD ESL's) and 100/100 work great for you (knowing Bedini, they probably have the same gain), but the pairing of a 25w amp with a 100w may or may not work with anyone else's loudspeaker. They certainly wouldn't with my Magneplanar Tympani T-IVa's!

I have a B&K Sonata 5ch amp,  150W×5 which I used with an active crossover, it has outboard trim but I used the gain on the X-over to set the levels and the x-over points
That's how it's done in a pro-audio environment (for good reason)
Sounded super clean and strong
I would sell it if you're interested 

The question boils down to this: if you had the ability to measure power consumption of white noise (equal amplitude across the audible spectrum, not necessarily 20Hz to 20kHz, if you could do it for 50Hz to 10kHz that would be a sufficient demonstration) by the two halves of a bi-amped speaker, what would you see?

Since the crossover point between the low frequency section and the mid/hi frequency section of a speaker will almost always be in the lower part of the 50 Hz to 10 kHz range, most of the energy of white noise occurs at frequencies that would be above the crossover point. So most of the energy of white noise would be delivered to and reproduced by the mid/hi section of the speaker. The spectral composition of music is very different, of course.

With music, per my earlier comment, if the crossover point of the speaker is 350 Hz both amps would typically have to supply approximately equal amounts of power. If the crossover point is significantly less than 350 Hz the high frequency amp would typically have to supply more power than the low frequency amp. If the crossover point is significantly higher than 350 Hz the low frequency amp would typically have to supply more power than the high frequency amp.

With music this relationship will of course vary somewhat from recording to recording and from moment to moment. Which is why I used the word "typically," meaning that it would hold true the majority of the time.

Regards,
-- Al

I am using one stereo amp on each speaker. Left for mid highs and right for bass cabs.  The meter is always higher on mid highs.  Same amp.  Crossdover point between upper bass driver and lower mid driver is 230hz.