If you can hear a difference of two amps (or any other technical gear in audio), you will measure the difference. If you cannot measure a difference, then there will be no difference and all your hearing was illusion.
Lots of scientific studies have been made in the field of hearing. And a healthy ear will indeed distinguish very tiny differences of delay time between the two ears, tone pitches and generally our ears are very sensitive with a great dynamic range between extremely quiet sounds and very loud noise.
But there are not only the ears, who are the receptors of the audible world around, but there is also a brain and its hearing areas. And the brain will always make its own interpretation of the neuronal information the ear brings to him. This is probably the greatest part of the work our brain does continuously: to sort and to interpret all the information our sensory organs bring to him.
And it is not difficult to consternate our brain and to let it misinterpret sensual informations. Probably the most perturbing factor are our expectations! We will hear and we will understand, smell and so on, what we expect to hear, to understand, to smell. There are also lots of investigations about this item.
So if you want to do some objective tests, you must eliminate all expectations as good as possible. Any scientific test design must have been done so. To test tone pitch differences or time delay differences it will be easy, because there is simply no expectation if the next tone presented will be lower of higher or will be heard coming from a certain direction.
But if you will see the brand name of the amp or/and its appearance will be impressive, you will expect it will sound better. Immediately and unconscious.
So only a double-blind-test will guarantee a certain level of objectiveness. DBT of cables always could reveal, that there will be absolutely no difference between ultra cheap and ultra expensive cinch-cables and microphone-cables for example.
I would say, that if an amp exceeds some certain thresholds in THD, Noise, IM, channel separation, flatness in frequency, frequency range and so on, it will sound very good. For example, if its noise-level will be around -90 dB, you will hear no noise when you hear music at normal sound level. If the noise level will be better, -100 or -110 dB, the amp will be better from its specs, but at normal sound level you will hear no difference in noise.
So if you will have to look for the quality of an amp, you will look for its specs and you must know, witch level the construction will exceed in all its details as minimum that all sorts of distortions will remain unaudible (at normal hearĂng sound levels). Any sort of distortion beyond ca. -90 dB will not more audible for all I know.
Another criteria could be its robustness, capability of uninterrupted service, especially if the amp should be used for PA.