Bond,
Specs are only guidelines and alone do not determine level of performance. The only way to determine that is to listen and compare.
In my case, if after listening carefully for a while to a particular configuration I identify an area that I feel could improve based on listening to reference systems, live events, or whatever I can identify as a meaningful reference for comparison, then specs are a useful research tool to help weed through options and identify choices that based on specs might perform better in my system specifically compared to other highly regarded pieces.
Even then, the only way to know for sure is to experiment.
In the case of my amp upgrade, I moved from a 360w/ch Carver to a 120w/ch Musical Fidelity and knew eventually I wanted to get back to a high power amp without losing the benefits the MF brought to the table.
The power rating of the amp and its importance in being able to drive the OHMs optimally was the main factor that drove me to look at an upgrade eventually. The power differential was cut and dry. The MF amp sounded better than the Carver in every way, but there was less power now available for fairly power hungry speakers.
Based on power and current alone, there were many choices to pick from, so I looked for other factors on paper that might make a difference. Its still always something of a risk changing though until you actually try something different and hear the results, which may be better or worse or more commonly better in some ways but not as good in others.
I have heard some claim that they can always hear an improvement in sound quality with an amp with higher input impedance compared to lower. Technically this makes sense. Practically, how much difference is there and is it enough to matter to most? I don't know. Also other factors contribute to sound so it is risky to base a choice perhaps on any one specification alone.
Fun stuff (and potentially EXPENSIVE)! Seldom ever cut and dry however.