Like one individual changed his 125 watt power amp to a 250 watt, with a higher damping factor (claimed), and the change in sound was amazing. This is a hypothetical situation but it happens all the time.
But is this really the case?
There are many reasons why it happens all the time. For example, may be his/her amp(s)
1) Has damping factor too low (say <50) for their speaker/wiring system.
2) Cannot handle low impedance and/or phase angle so it cannot sustain the current required by the speaker on a moment by moment basis.
3) Low quality, i.e., high distortions of any sorts, subpar frequency response even under optimal conditions.
4) Poor conditions, i.e. aging electronic components, capacitors, high contact resistance (age, oxidation, loose etc.).
5) Not enough power for the demand (somewhat related to 2).
6) Placebo effect, the ones that costs more, heavier, better looking, or preceived ideas acquired from hearsays, brand recognition such as xyz has a warm/tube like sound, tend to sound better.
7) Exaggeration - people tend to use expressions such as day and night, amazing, jaw dropping, huge, in order to make their point, when the difference may be subtle but perhaps clearly audible.
8) Not volume match, even a 1 dB difference in volume level, while not clearly detectable, could make the louder one sound better.
IMHO, there are many more factors than listed above that could cause one amp sound better or worse than the other even when both have similar specs on paper, the last two probably are the major ones in most cases.