In principle - yes, but actual volume is also dependent on your speakers and other factors. When comparing amps there are alot of variables to consider, in particular how many channels are being driven (so an amp that can drive 5 channels at 100W is more powerful than one quoted at 100W for a single channel). There are other factors too including THD figures are quoted at, so in general be careful when looking at quoted figures.
If you have a specific example in mind plesae post it, there are many members with far more technical knowledge than me that can advise.
EDIT: as GW43 correctly stated while I was typing, the relationship is not linear, twice the power does not equal twice the volume.
Repeating what GW43 said. Power and Volume are not linear, meaning to double the volume takes roughly 10 TIMES more power, and to raise the volume slightly, take DOUBLE the power.
In your example, the 100 watt amp would only be slightly louder than the 50 watt amp; all other things being equal.
But there is this knob on the front of your amplifier, and it you want it louder, you just turn the knob up. The maximum reasonable volume of virtually every amp and the absolute maximum volume are both way more than any reasonable person needs.
Likely long before you reach maximum volume both the amp and the speakers are going to be dangerously distorted.
So, if all that power only brings a slight increase in volume, what good is it? What do I want it for?
With amps, we seem to be obsessed with power, but amps don't create power. The deliver voltage and as a result current is consumed, and when current is consumed, power is also consumed. So, in short, we feed speakers voltage and they consume power. In fact, Power is Voltage X Current.
Using simplified calculations, a 50 watt amp has a maximum voltage of (+&-) 20 volts. A 100 watt amp, again somewhat simplified, has a maximum voltage of (+&-) 28 volts. [V = SqRt(PxR)]
So, we can feed 20 volts to a speaker from a 50 watt amp. But as the average signal level gets louder, peak voltages reach to and exceed that 20 volt limit. This is referred to as clipping or asking an amp to deliver more voltage than it is capable of.
But, with a 100 watt amp, at the same volume level, we can send peaks up 40% higher than with a 50 watt amp. That is what you get with more power. The ability of music peaks to reach up higher without hitting the ceiling or voltage limit. This extra voltage is called head room; a higher powered amp buys you more head room.
Naturally, if the music reaches up and is cut off by the voltage limit, the music sounds distorted. If clipping gets too extreme, for an assortment of reasons, you can damage your speakers and possibly your amp.
So, when you go from a 50 watt amp to a 100 watt amp, what you gain is not an additional 50 watts, but 40% more voltage. You can output a 40% higher signal with the 100 watt amp.
We measure all this in power, but in the end, it is really about voltage.
There are an assortment of other factors that come into play with a larger amp, but for the moment, they just confuse the issue. Perhaps, we can expand on them later.
Awesome reply guys, thanks for taking the time to clear it up. I was asking because i recently purchased some AE Aego M's and thought they would be twice as loud (and some) than Logitech's Z-4s, however that is not the case! The max volume is only marginally louder which suprised me; it now clears it up though. Bit disappointing!