First of all, individuals vary in their ability to detect volume differences. All of us vary in this ability depending on the frequency of the sound.
With that said, in general, one decibel is usually described as the smallest change in volume that can be detected - but since a decibel is a fixed unit, it ignores the frequency dependent nature of our hearing.
When talking about power, a 3db increase represents twice the power of the original reference and a 3db decrease represents one half the power of the original reference. A 10db increase represents ten times the power of the original reference, and a 10db decrease represents one tenth the power of the original reference.
Acoustically, we perceive a 10db difference as either twice or one half a difference in volume. So, if we want to double our perceived volume we need to increase the power output by a factor of 10. A 100 watt output sounds twice as loud as a 10 watt output. To sound twice as loud as the 100 watt output, we would need 1000 watts.
Can you hear a 3db difference? Barely. If you have an amp with 4 output tubes, take out two of them (the two outside tubes to make sure since pairs on the same side of the output transformer are usually arranged this way). Now your amp will produce roughly 1/2 the power - a 3 db decrease in output volume.
It won't be that easy to hear a difference. I have an Acoustic G100T that does this with a half power switch that cuts out two of the output tubes. Operating with four tubes sounds like the bass has been boosted very very slightly over two tube operation.
That's why instead of increasing wattage capacity, it's normally more effective (cost wise) to increase volume by using more efficient speakers. And why I personally avoid high wattage handling in my speakers - with those speakers that handle 300 to 600 watts, the trade off is a loss in efficiency requiring more watts to make up for it to keep the output volume the same. It's kind of like the dog chasing it's tail.