Why would a lower ohm rated speaker be more difficult to drive if it requires less watt than an 8ohm speakers?
Lower ohm rated speakers
do not necessarily require less watts than an 8 ohm speakers. If you consider two speakers with similar characteristics except one is 4 ohm and the other is 8 ohm placed the same way in the same location, how much power they require will be determined by their sensitivity. You have to be careful with the specification however, because sometimes they specify sensitivity in X dB at 1W at 1 meter, other times they specify it in X dB at 2.83V at 1 meter. In terms of X dB 1W at 1 meter you can make a direct comparison while in the format X dB 2.83V at 1 meter you would have to subtract 3 dB for the 4 ohm speaker when you do the comparison because you need double the power to gain 3 dB of sound pressure.
For clarity, consider:
Scenario 1 - Both speakers are specified 87 dB 1W @ 1 meter in an anechoic chamber.
In this case they both require the same power to produce the same sound level.
Scenario 2 - Both specified 87 dB 2.83V @ 1 meter
In this scenario, they are telling you you need to apply 2.83V to the speaker at a certain frequency to produce 87 dB at 1 meter distance so applying one of the formula I listed before:
Power=VXIXCos Θ or (VXV/Z)XCos Θ (V=voltage, Z=impedance)
You can see that the 4 ohm speaker will need twice as much power as the 8 ohm speaker does. If you try it with 2.83V, and assume CosΘ=1, that is the voltage and current phasors are in phase (rarely happen), then:
Power=2.83X2.83/4=2W for the 4 ohm speaker, or 1W for the 8 ohm speaker to produce the same 87 dB at 1 meter.
In order to determine if your 4 ohm speaker requires twice as much power as 8 ohm speaker with similar sensitivity specifications you have pay attention to how they specify them. So once again, if the specifications say 87 dB 1W 1 meter, then you can compare it directly to an 8 ohm speaker that is specified 87 dB 1W 1 meter but if it says 87 dB 2.83V at 1 meter than you need double the power.
You also asked why 4 ohm speakers are more difficult to drive. One of the reason is simply because at a given voltage they will draw twice as much current as an 8 ohm speaker does. That is not always a problem if the speaker's sensivity is high enough to make up for it.
Having read your post again, I thought you may be wondering why a well design amplifier can deliver more power into lower impedance load. Well designed power amplifiers generally have larger (relative to say, receivers and integrated amps) power supplies and electronic components including the power transistors to handle the higher current demand by lower impedance speakers. Since power increases with the square relationship of current and decreases only linearly with impedance, there is an net gain of power delivered to a lower impedance load (speaker). I hope this clarifies things a little.
