There are waaay too many factors at play to point to one source being the true culprit if you look at this in a general sense. Speaker efficiency is one aspect, the type of amp the other. With tube amps, the volume output can change wildly for similarly rated amps, and I'd say the big reason for that is how the amp is biased and through what kind of speakers (and how many) the sound is coming from. An easy example is a 5150 without a bias mod vs. a 5150 WITH a bias mod. A cold bias stock 5150 will be a LOT quieter at the same knob position as a 5150 with a hot bias, because more current is being supplied to the amp with the hotter bias...But, both are still "120 watt amps" and both use 4 6L6 tubes.
In the case of solid state amps, each manufacturer can measure and state power rating a bit differently from one to another, such as using "120 RMS" as an amps rating, or just "120 watts"...Which could mean RMS or peak.
Now, add to all this the speakers and their effeciency rating...Something like a Celestion Vintage 30 will no doubt probably have a better sensitivity rating than a cheap low quality speaker. Say a V30 has a sensitivity rating of 101dB @ 1 watt at 1 meter...A cheaper quality speaker may only have a 98dB sensitivity @ 1 watt @ 1meter. 3dB is perceived as twice as loud to the ear...so even 2 speakers both rated at 100 watts are heard, the one with greater sensitivity will be louder...This is assuming the power rating for each utilize the same measurement methods.
In your specific case, I'd equate your issues to the quality/price of your amps. To be honest, both amps are cheap, lower quality amps that are no doubt driving cheap, low quality speakers. And, the cabs you are using I would assume match the quality/price point of the amps, so again it's more than likely cheap speakers. Whichever amp/speaker combination is louder is more than likely due to the wattage ratings and speaker sensitivities used in the louder setup to be advantageous to your overall volume level.
If you want a budget cab, I say:
1.) buy used
2.) Make sure it has decent speakers in it
Something like a used Avatar cab with some type of quality Celestion speakers (Avatars commonly come with Celestions). Or something used with quality Eminence speakers (Eminence makes a lot of different speakers, some of which are cheapies).
If you could find a deal on a decent 4x12 with some WareHouse Speakers, that may be good, too. Warehouse Speakers makes a killer V30 clone (I actually like the Warehouse clone better than the original).
If I were looking to buy a low cost setup that I felt would adequately meet my needs, I'd personally look at something like Peavey Valveking and an Avatar vintage 4x12 with Celestion Vintage 30's, preferably buying both the head and cab used. If bought new, you'd probably be looking right at 1000 for both, and maybe 500-700 for both used? I don't really know current market pricing on these items used.
Also, the new Jet City 100 watt head looks interesting (Soldano designed), but it's cost new is around 800 US.
Finally, in terms of cheap vs. expensive amp heads, I would wager that in this scenario - in terms of tube amps - it will be country of manufacture and the quality/price of the components to be the difference in price, not necessarily guaranteeing the cheaper one to be quieter through the same cab - assuming both tube heads are biased the same and use the same tubes, ohm load, etc. which would be the best way to truly compare.
P.S. I'd also add that your disclaimer that tone isn't as important as volume may be self defeating. As you try to EQ the amps to sound the way you want, you may be taxing the amp beyond it limits and reducing the amps power/output by doing so (like trying to run too much low end or something). Finding an amp that is voiced the way you like that sits in your band mix well can go a long way. It's not always about power/volume.