Impedance and resistance aren't the exact same thing, and for headphones specifically, impedance is what is measured. In any case, it really depends on the amp design. On speakers, it's more straightforward - the impedance range is between 4ohm to 8ohm in most hi-fi applications, with the exception of car subwoofers that may have 2ohms, so generally lower impedance means higher output. Go too low however and your amp might be producing a lot of nominal power, but might not have enough reserve juice for dynamic passages. Since the rated impedance is
nominal - depending on the design of the drivers, and it can also be affected by the crossover - many don't realize that depending on the frequencies playing impedance may change, so at any given point in the playback, your 8ohm speaker might be dipping a bit lower or higher, and this can be a bigger problem with 4ohm speakers since dipping lower means the amp driving it will hit its limits however briefly. This is why, between two speaker amps that measure the same way on a test tone, the one with the huge power supply that doubles its output when the impedance is halved might usually sound better than an amp that only produces less than 50% more power (when the impedance is halved). This is why not all Class D amps are as tiny as the Sonic Impact, or even if the circuit board and heatsink are tiny, the power supply is considerably bigger.
With headphones it's a bit trickier because of the much, much, much wider range of impedance from 16ohm to 600ohm, and as such some amps are designed to deliver more voltage to produce more power for high impedance headphones, while some are current drive amplifiers designed to deliver more power at lower impedance. It's not unusual for example to find a headphone amp that produces more power at 300ohm while another produces most of its power at 32ohm, although
very generally given they are both powerful enough to get two headphones to a proper listening volume it is likely for the 300ohm headphone to perform well with both while the lower sensitivity, current-hungry headphone will sound less dynamic with the voltage-driven amp. There are different advantages and disadvantages to either design that affects headphones more than speakers (such as hiss on too low impedance headphones with the wrong amp) so it really depends on which ones the manufacturer would rather deal with for a given application.
