Two equations tell the entire story. Watts=VoltagexCurrent, and Watts=Current(squared)x Resistance.
So as has been stated earlier an amp that is not current limited will double its power as the impedence is halved. So if an amp is rated at 200 watts into 8 ohms it must produce 400 watts into 4 ohms and 800 watts into 2 ohms.
But that really is only half of the story. To answer the question about how this impacts the sound you have to know what the impedance curve is for the speakers you have. I used to own Thiel 3.6s. They are nominally 4 ohm speakers but there is a point in the lower midrange where they dip to about 2 ohms as I recall. That means if you are driving a current limited amp (say 100 watt into 4 ohms rated amp) close to its limit, the speakers will be demanding 200 watts in this midbass region. If the 100 watt amp is only rated at 150watts into 2 ohms you could be running into clipping and a clear audio distortion. So high current designs are not necessarily required for many well behaved speakers. There are lots of high end speakers some cause trouble other wont.
So as has been stated earlier an amp that is not current limited will double its power as the impedence is halved. So if an amp is rated at 200 watts into 8 ohms it must produce 400 watts into 4 ohms and 800 watts into 2 ohms.
But that really is only half of the story. To answer the question about how this impacts the sound you have to know what the impedance curve is for the speakers you have. I used to own Thiel 3.6s. They are nominally 4 ohm speakers but there is a point in the lower midrange where they dip to about 2 ohms as I recall. That means if you are driving a current limited amp (say 100 watt into 4 ohms rated amp) close to its limit, the speakers will be demanding 200 watts in this midbass region. If the 100 watt amp is only rated at 150watts into 2 ohms you could be running into clipping and a clear audio distortion. So high current designs are not necessarily required for many well behaved speakers. There are lots of high end speakers some cause trouble other wont.