Why do I get less power from cheaper batteries?
Your hypothesis #1 is the correct one. 9-V batteries are not designed to deliver high current and heat some heating coils. Given the battery's small physical size and necessity to have 6 primary elements inside (6S configuration), they just can't possibly deliver high current, and are intended to use in long-lasting low-current consumer devices as smoke detectors and DMMs, with consumption in a fraction of milli-amp. Their capacity is 300-400 mAh, and devices are expected to last years. So the internal impedance is of least concern as long as the battery serves its main purpose. The actual difference in internal impedance between your two batteries is not that much, according to your measurements, no more than a factor of two.

And the hypothesis #2 is essentially the same as the first one. Cheaper battery is likely using less sophisticated and less fine-grained materials that result in higher internal impedance, which results in less output voltage under the same load, and therefore "less power".