a Power vs Volume Question

Each doubling of power increases loudness by 6 db. The ear perceives a 10 db increase in sound level as a doubling of volume.

Actually a doubling of power is 3dB, a doubling of voltage is 6dB.

Loudness and volume are the same thing.

It should read "Each doubling of power increases sound pressure levels (SPL) by 3 db. The ear perceives a 10 db increase in SPL as a doubling of volume."

Further to Herman above, each doubling of SOUND PRESSURE level (i.e. spl), i.e. what we "listen to", is 6dB. You need four times the "power" to achieve double sound pressure -- in fact twice "as loud". Yr mic should record +6 dB when your power rises 4times.
In other words... on paper, going from 200W to 300W gives you an extra 1,4dB. That's assuming, of course, that the speakers can take 300W continuous -- which they usually can't.

Twice the power is a 3db increase.
10db is twice the volume or loudness.

Both loudnes and volume are perceptual terms correlated with acoustic level. The knob you twirl is a level adjuster.

Not all amps have the same gain. For example, McIntosh, IIRC, rated their MC 60 at 60 watts RMS 20- 20 kHz with a .5 volt input, whereas the Dynaco 60 watt amp required a 1.5 volt imput to reach that level, so its gain was much lower. (I think the days of the MC 60 were before the JASA style sheet required capping the H in hz for Hertz or the B in db for Bell.) Two other things to look for in amp specs is power bandwidth and distortion rating. Those two numbers can make two different 200 watt amps quite different.

As to the OP, for most practical levels and with equal quality amps, there shouldn't be a difference in SPL whether the amp is 200 or 300 watts, unless the speaker represents a very difficult load.

db

each doubling of SOUND PRESSURE level (i.e. spl), i.e. what we "listen to", is 6dB. You need four times the "power" to achieve double sound pressure -- in fact twice "as loud". Yr mic should record +6 dB when your power rises 4times.
In other words... on paper, going from 200W to 300W gives you an extra 1,4dB.

Greg, I believe you are a bit off in your analysis.

Incorrect: Doubling SPL is not 6dB, it is 3 dB,

Correct: Double it again for 4 times and that is 6dB as you stated.

Incorrect: Going from 200 to 300W is not 1.4dB, it is 1.76dB.
dB = 10 log (300/200)
dB = 10 log 1.5
dB = 1.76dB