All those things you cited above are correct, but you last sentence is false, due to your misunderstanding of how things work in terms of "W" vs sound pressure level, that is, it is not a linear relationship, and you need a lot more "W" to make a significant difference in terms of the "loudness" you will perceive.
It is important to understand that in practical terms, 2 times the power output = only 3 dB difference in sound pressure level and in most cases, it is generally recognized that one needs to have at least 6 dB, or up to 10 dB higher spl to perceive "twice" as loud.
In terms "how loud" sound pressure level, we use the log scale because it is not a linear relationship.
3 dB = 2 times
1 dB = 1.258 times
-3 dB = 0.5 times
So, the S970H, 90 W, compared to the S570BT's 70 W, the ration is about 1.28, that will give you just 1.07 dB more in terms of sound pressure level
Between the two AVR, for you to hear the same sound pressure level, the difference is just 1 in the volume dial. That is, all else being the same, with the S570BT, if you set the volume to -20, with the S970H, you only need to turn it to -19. Practically no difference.
If you want to play with this, use an online calculator such as the following:
gain factor ratio gain conversion to level in decibels dB amplitude voltage gain conversion to factor field quantity dBu dBm dBW dBV dBmV dBµV dBu energy size power voltage damping attenuation amplitude amplification acoustic intensity sound pressure factor ratio voltage gain powerloss level...
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