What is responsible for amps to have different dynamic range?

Ok, the question is not fully coherent. I did not quite know how to put it in one sentence. I have currently two amps - one solid-state and one tube. The question is not specific to these two amps. I am using a headphone to listen to both of them through SE output. The source (both digital and vinyl) is the same for these two amps. So the only difference when I am listening to any song is the amp. Now, when I am listening and come across a section in the song where the dynamic range is big (the softer/quieter part/note suddenly transitions into a loud note/part ), I get the following experience
......... (Gradual increase to louder note and the difference between soft and loud note is'nt pronounced)
Amp 1 - ..
..
..... (Softer note)






Amp 2 - ....... (Sharp increase/slope and the range is also bigger)
..
..
..
..
..... (Softer note)


One example song where this is very pronounced is . Now I am listening to the same volume level on both. Amp1 is the solid state amp and Amp2 is the tube amp. I am pretty sure there would be many solid state amps that would have such characteristics as of amp 2. My question is, what quality/component/stage in an amp actually imparts this quality of sharp dynamic range? The only difference in this setup are the amps and rest is constant, so this has to be a characteristic of the amp.