I agree. I think that power (including current, headroom, etc.) is the only difference between amps. I don't think that an amp has a "characteristic" sound otherwise (nor that it should.)
respectfully, I disagree with some of that statement, an amplifier
shouldn’t have a "characteristic" sound (that is, if you are going for absolute fidelity, if you’re going for just something that "sounds good" well....

), and as it has been pointed out many times before, they often don't.
However, as an example, in my post number
37, I referred to the specs of a few amplifiers to the effect that (within a bandwidth of 10Hz or 20Hz to 20kHz) the frequency response can deviate up to 3dB above and below a flat response, so that would mean that two frequencies that are the same level on a recording could have up to 6dB deference in volume when played back, perhaps a somewhat extreme example, but still possible.
Personally, I feel that two amplifiers can sound deferent, there is
no way the deference could be "night and day".

(hope I did'nt start a flame war

)