We have been through this many times before.
Doubling the amplifier power will double the acoustic output of the speakers (in acoustic watts) giving a +3dB increase in measured sound pressure level.
(In reality speakers tend to compress so there are some losses, so in the real world the difference will probably measure a little less than +3dB.)
Now the human ear is normally believed to be sensitive enough to hear a 1dB change in level, but this is with a test tone under lab conditions. Make that a music signal, in a domestic living room and you will be lucky to hear a change of +2dB.
So, realistically a +3dB change in level, in those conditions, represents the smallest increase in in level that is clearly identifiable as an increase as such.
And to achieve that increase you need twice the amplifier power. It depends how you define significant, but twice the power most definitely does not sound twice as powerful.
For reference, science requires a +10dB increase (10 times) in power to sound twice as loud but, modern subjective analysis suggests that, around +8dB sounds twice as loud to most people. This is hugely subjective so views will and do vary.