Thank you DaveAceofBass for taking the time to reply.
BadExample pointed out that you and I might simply be having a semantic disconnect - when I say "power distribution", I'm talking about how the amplifier's output (wattage) is distributed between the two cabs. If you are talking about something else, like how loud each cab will be, then we're talking about different things.
That being said, here are my replies to your post:
Suppose you have a head that puts out 250w at 8 ohms and 500w at 4 ohms. You hook up two 8 ohm cabs...Brand A has a 210 w/ tweeter with a sensitivity of 95 and Brand B is a 112 w/ 6 inch mids and tweeters with a sensitivity of 105. Hypothetically the 210 should be louder, but the 112 is clearly louder.
Agreed.
Now suppose that head can go as low as 2 ohms. The same cabs are used, except this time you use a 4 ohm version of the 210 and the 8 ohm version of the 112. You would expect the 4 ohm cab to be louder due to more speaker surface and lower impedance. However, in this case the 112 is still significantly louder. This is one of the exact scenarios I've experienced, but not the only test.
Ignoring the idiosyncracies of the individual impedance curves, in this example the theoretical 500 watts coming from the amplifier would be distributed as follows: 333 watts into the 210, and 167 watts into the 112.
In this scenario, the 95 dB 210 cab would theoretically be hitting about 120 dB, and the 105 dB 112 cab would be hitting about 127 dB, ignoring thermal and mechanical compression. Calculating the combined SPL of the two is more math than I'm willing to do right now.
Usually the greater the speaker size of the cab, the louder it is. So a 410 would be louder than a 115, as there is more speaker surface. But I don't think that's what is in question...it's how much power each can receives, right?
That's what I've been talking about, yes, how much power each cab receives.
Two well known amp companies have explained this to me directly. By hooking up two 8 ohm cabs, the amp "sees" 4 ohms, but that doesn't mean a 500 watt amp sends 250w to each cab. Imagine you have a faucet and you connect a Y-shaped valve to it, where one side of the Y is much larger in diameter and the other much smaller. When you turn on the water, the majority of the water flows to the larger diameter opening, but some water is still diverted to the smaller opening. This is how the amps work, in my experience, and from what I have learned from experts.
In this analogy, if each is an 8-ohm cab, then (ignoring the idiosyncracies of their individual impedance curves) both sides of the Y are the same diameter. However if you are combining a 4-ohm cab with an 8-ohm cab, the 4-ohm cab's side of the Y is 1.414 times greater in diameter (which works out to double the cross-sectional area).
So your hose analogy is very close, but if the impedances are the same, then the hose diameters would be the same (again, ignoring the idiosyncracies of the individual impedance curves).
Now let's suppose I am wrong and each cab does get 250w in my hypothetical scenario. Even if that is the case, the speaker with the higher sensitivity will be louder. I can tell you this from first hand experience. Now even if both speakers received the same power, the main conclusion that we all need to know is that the speaker with higher sensitivity will be louder.
Yes, how loud each cab will get is a function of its efficiency and how much wattage it sees.
But in my opinion, there is another conclusion that might be more important than which cab is louder: Will one of the cabs be in danger of being damaged??
Suppose the cabs in your second example above, the 4-ohm 210 and 8-ohm 112, are both rated at 300 watts. If you're driving both cabs in parallel with your 500 watt amp, knowing that the 210 would theoretically be seeing 333 watts at full power might be valuable information that would keep you from pushing your rig too hard.
(If we wanted to be thorough we would look at the mechanical power handling as well, but we'd probably have to rely on making educated guesses.)
Keeping cabs from being inadvertently overpowered is why I have focused on power distribution to the cabs, rather than on how loud each cab gets.