I've had it explained to me this way (and I could be wrong so if someone could verify this): If an amp, of any wattage rating, has the capability to generate double its wattage rating into successively smaller ohm loads (200 watts into 8 ohms, 400 watts into 4 ohms, 800 watts into 2 ohms) it means that the amp has the ability to deliver the maximum amount of current needed to drive the speakers at a given volume. An amp with higher wattage into 8 ohms, say 250 watts, that can successfully "double down" its power rating into lower ohm loads, can push the speakers to a higher volume level without distorting than say a similar quality amp with only 120 watts into 8 ohms. The end result will be a higher decibel rating in the room, say 106 db over 100 db, without distortion.
The speaker rating for wattage, say 50-200 watts into 8 ohms, is to tell you that with a certain wattage amp the speakers can theoretically be driven to a certain db level without damage. If the amp cannot provide the necessary power as the impedance of the speaker changes during musical transients or as you raise the volume level, the amp will "run out of punch" and clip because it does not have the power to push the current the speakers need. This is bad because the "clipped" waveform will eventually fry your speakers. If the amp is "too powerful" (is there such a thing?), meaning the amp is rated higher than the wattage rating of the speakers, then the opposite can happen. The amp has the ability to push more current into the speakers in order to generate higher volumes and to react to dropping impedance loads. At low volumes this effect manifests itself as "bass control, increased soundstage" and the ever-searched-for "air". At high volumes (And I mean ear-splitting volumes), you can blow (or melt the voice coil if it heats up) the speaker because you have exceeded the transducer's ability to change electrical current into physical motion. The rule of thumb that I go by: always keep your weakest link moving downstream. With a powerful amp to tame your speakers you can be sure that most of the information is getting through. Plus you go easy on your electronics (was your car optimized to run at the redline or at about 2500 rpm?). In your case, seek out a really good 250 wpc amp and you will be very happy.
The speaker rating for wattage, say 50-200 watts into 8 ohms, is to tell you that with a certain wattage amp the speakers can theoretically be driven to a certain db level without damage. If the amp cannot provide the necessary power as the impedance of the speaker changes during musical transients or as you raise the volume level, the amp will "run out of punch" and clip because it does not have the power to push the current the speakers need. This is bad because the "clipped" waveform will eventually fry your speakers. If the amp is "too powerful" (is there such a thing?), meaning the amp is rated higher than the wattage rating of the speakers, then the opposite can happen. The amp has the ability to push more current into the speakers in order to generate higher volumes and to react to dropping impedance loads. At low volumes this effect manifests itself as "bass control, increased soundstage" and the ever-searched-for "air". At high volumes (And I mean ear-splitting volumes), you can blow (or melt the voice coil if it heats up) the speaker because you have exceeded the transducer's ability to change electrical current into physical motion. The rule of thumb that I go by: always keep your weakest link moving downstream. With a powerful amp to tame your speakers you can be sure that most of the information is getting through. Plus you go easy on your electronics (was your car optimized to run at the redline or at about 2500 rpm?). In your case, seek out a really good 250 wpc amp and you will be very happy.