It depends on what you are referring to. +3dB is not 2/3 of the original power. Scroll down to the middle of THIS PAGE to see a chart of ratios and factors vs dB both for voltage, and for power. A 2:1 ratio is a 3dB power difference, and a 6dB voltage difference. Your noticeable difference and perceived doubling references are correct as I know them.
Calculations of dB are also done with log(base 10) values, not ln values.
Got my radioactive decay half life and cut off frequency calculations mixed up
So the 3db point is only important because the amp output voltage will drop by 1/2 at this point. In other words, it really isn't an ear thing at all.
3db is a perceivable difference
10db is perceived as 2 times as loud.
All of this must be taken into a great context of how the measurement was made.
Even after you do this, just making lots of noise isn't necessarily a good thing. The noise has to be pleasing!
Sadly, there are no standards or specs you can go to for a measurement of "good useable output".
Typically, what speakers like 2-way tops do is drop off of the LF driver when pushed. The HF driver can almost always produce more SPL with less power and without burning out the driver. This isn't a good thing and it sounds horrible.... but you can still ligitametly say your speaker is putting out 133db at 1 meter and not be lying.
Personally, I think an SPL reading with filters on a few bands would be more useful in determining how well a speaker works, but even this would not include distortion issues.
More expensive speakers tend to be able to put out pleasing sound at high SPL because they stay linear, and don't distort even when loud. Less expensive speakers may be able to generate high SPL, but don't sound as good doing it.