It's a matter of power. Certain phones need different amounts of power to be driven correctly, and then also certain amounts of **voltage swing (potential difference) to be driven to a certain volume (sensitivity)...
where P = Power, I = Current and V = Voltage
we see that P/V = I, meaning that power and current are directly related whereas voltage and current are inversely related (i.e. higher power = higher current, lower voltage = higher current).
and then we have ohms law which is (swapping letters around to match the above)
V = IR
where R= Resistance.
P = I(IR) = I^2R thus
P/I^2 = R
We see that Power is directly related to the resistance, and current is also directly related to power, but they (power and resistance) are inversely related. I.e. Low Resistance = High Current required to get desired power.
A lower impedence version of the same phone will require a larger amount of current to be powered and we also see that (Via V=IR) that a larger current is required to achieve the desired voltage swing.
But when you compare different models theres things like sensitivity and efficiency.
That's the basics of it though.. You'll also have a higher noise floor on low impedence versions of the same phones because they are running "hot" (i.e. more current). Volume knobs work differently though (they are a variable resistor) which will squeeze more power from the same current thus driving the phones louder
Disclaimer: its 5:34 am and my maths might be wrong because of this (and so might the concept). Feel free to correct and i will edit/remove
I've tried to clear up my english as much as possible