I am not sure if generalising this is so easy since if we look at the system approach, the weakest link is what you would upgrade. My order of priority would always be Source > Room+ Speaker > Speaker + Amplification in sound
IF the source itself is of lower sound quality then one would not even know where the problem is ! And very often its the speaker and amplification which gets the blame.The source will literally govern the sound quality since the smallest of deviations is amplified several times down the chain till the speaker, hence it has to be the best you can afford to own.
Speaker + Room ie the right speaker for the room and optimally placed in accordance to seating position is the next in priority most setups are not optimised for the room , and this could be due to various reasons , right from the constraints of aesthetics and space to lack of the knowledge.
This is followed by the right Amp for the speaker ie which has the right power and resolution for the speaker and matches with it both sonically as well as electronically.
Hence the key before one even thinks of an upgrade is figuring out the "weakest link" in the system and sometimes it very well could be the speaker. Although in most cases, even in this forum, its the speaker which is the most well researched hence may be the last in order of priority
I am not mentioning cables/power/vibration etc since those are for the last 5% after all of the above has been done.
So how does one know they have the best 'matched' amplification
If you have a source you can trust then you can do an A/B evaluation. but for most of us who cannot do the A/B it has to do with experiences of others whom we trust and also in case there is a recommended combination eg could be how they are exhibited during Hifi Shows ( not showrooms
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