@kuribo But you can’t tell how an amp really sounds just by looking at measurements either. You can have two amps that measure similarly but sound completely different. Why? Because we don’t have near enough the measurements that can measure everything that has an impact on sound.
No, you can't tell with any certainty how an amp sounds strictly from measurements but you can tell certain things about it's performance, whether it adds distortion, how much, where and when, how it's performance varies with frequency and load impedance, etc.
Sound similarly to whom? To everyone? Doubtful and not realistic. There are too many biases and other factors that enter into subjective impressions.
What measurements are we lacking? Please explain what it is that we are not measuring. Just because something sounds the same to you doesn't mean it is the same, or that it will sound the same to someone else. Of course, there are things humans can't hear, and it is possible this lack of hearing can cause things to "sound" the same, if the differences are beyond audibility.
I ask again, why does it have to be a lack in what we can measure, why can't it be a difference in subjective perception?