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You don't mention anything about the speaker(s)? If the speaker can be maxed out with the smaller amp, that is as good as it gets. More power won't do anything, short of burning up the speaker coil.
Ron
An amplifier that has a 9.0V supply (not a weak little 9V battery) and an 8 ohm speaker produces only 0.77W at clipping. If its volume control is turned up higher then distortion harmonics are added until the output is a 1.54W square-wave.
You can turn the volume control on the 7W amp so the loudness sounds like the 1W amp but it will have no distortion. Clipping produces distortion.