To add to @almarg 's comments above, specs *are* important; perhaps the one that can be the most counter-intuitive is THD, as a very low THD spec is often an amp that doesn't sound nearly as good as one with a higher THD spec. I've already explained why above.
But bandwidth is real, output impedance is important (which isn't to say that the lowest output impedance is the best). Some speakers **require** that the amp have a higher output impedance, such as ESLs, horns and single-driver full range loudspeakers. Or any speaker where the designer has sorted out that he doesn't like brightness and harshness and so has designed the speaker for amps designed with intention to not have these properties (and often that means no feedback, so a higher output impedance). For more on this topic see:http://www.atma-sphere.com/Resources/Paradigms_in_Amplifier_Design.php
Now I discovered back in the 1970s that feedback wasn't all it was cracked up to be; that it could cause the amp to have a smaller soundstage (unlike the original recording; I know that from the use of master tapes) and be brighter than the actual recording as well. Since then I learned there is far more to it than just that simple concept- the use of feedback introduces about 7 different variables that the designer has to weigh out. FWIW the feedback formula doesn't offer a lot of guidance in that regard: in a nutshell most amps with feedback have a rather cursory application and ignore some factors (like RFI leaking into the amp via the speaker cables) entirely.
So of the specs that are suspect as to how much they contribute to good sound in an amplifier, IMO/IME the two top suspects appear to be THD and output impedance (IOW a better sounding amp might be one where these specs have higher rather than lower numbers).
Alternatively we also know that IMD is highly audible so low IMD specs are a very good sign but IMD is more pervasive than most audiophiles like to think about. In addition to the normal interactions between two tones, IMD also is a major issue in digital audio, but because the intermodulations are having to do with the scan frequency and the Nyquist Theorem, its called 'aliasing'. But as far as the ear is concerned, aliasing (the digital industry does not like to refer to it as a distortion, but that's exactly what it is) is an intermodulation (sometimes called 'inharmonic distortion' in the analog world) and so highly audible (the ear treats it as a brightness or 'crispness' and its still there if you turn down the treble, because the brightness is caused by distortion rather than frequency response). Of course if you look at the specs of a digital product, this form of distortion isn't listed. Again- the Emperor's New Clothes. Fortunately the digital world has been getting a better handle on this in later years; the more they do so the more natural digital is able to sound.
But bandwidth is real, output impedance is important (which isn't to say that the lowest output impedance is the best). Some speakers **require** that the amp have a higher output impedance, such as ESLs, horns and single-driver full range loudspeakers. Or any speaker where the designer has sorted out that he doesn't like brightness and harshness and so has designed the speaker for amps designed with intention to not have these properties (and often that means no feedback, so a higher output impedance). For more on this topic see:http://www.atma-sphere.com/Resources/Paradigms_in_Amplifier_Design.php
Now I discovered back in the 1970s that feedback wasn't all it was cracked up to be; that it could cause the amp to have a smaller soundstage (unlike the original recording; I know that from the use of master tapes) and be brighter than the actual recording as well. Since then I learned there is far more to it than just that simple concept- the use of feedback introduces about 7 different variables that the designer has to weigh out. FWIW the feedback formula doesn't offer a lot of guidance in that regard: in a nutshell most amps with feedback have a rather cursory application and ignore some factors (like RFI leaking into the amp via the speaker cables) entirely.
So of the specs that are suspect as to how much they contribute to good sound in an amplifier, IMO/IME the two top suspects appear to be THD and output impedance (IOW a better sounding amp might be one where these specs have higher rather than lower numbers).
Alternatively we also know that IMD is highly audible so low IMD specs are a very good sign but IMD is more pervasive than most audiophiles like to think about. In addition to the normal interactions between two tones, IMD also is a major issue in digital audio, but because the intermodulations are having to do with the scan frequency and the Nyquist Theorem, its called 'aliasing'. But as far as the ear is concerned, aliasing (the digital industry does not like to refer to it as a distortion, but that's exactly what it is) is an intermodulation (sometimes called 'inharmonic distortion' in the analog world) and so highly audible (the ear treats it as a brightness or 'crispness' and its still there if you turn down the treble, because the brightness is caused by distortion rather than frequency response). Of course if you look at the specs of a digital product, this form of distortion isn't listed. Again- the Emperor's New Clothes. Fortunately the digital world has been getting a better handle on this in later years; the more they do so the more natural digital is able to sound.