How much does power amplifier really matter comparing to other hi-fi components?

In my opinion this is a shifting % which is dependent on a few items. Budget, difficult speakers to drive and speakers that are extremely detailed. These items in my opinion will loosely dictate where the percentages of money should go assuming you plan on using a source, preamplifier and an amplifier. Source in vinyl is the platter, arm, cartridge, phonostage and cleaning machine. In digitial it is a transport, DAC and streamer.

A very modest budget will require more money to be placed into the speakers budget then followed by source. The pre and amplifier can be split.

A moderate budget will require the most money to be placed between the speakers and source, then followed by the preamplifier. As long as the speakers are friendly to amplifiers the amplifier will be last in line.

A budget where money is of little concern or you have spent the better part of a lifetime upgrading and now you are in that expensive category of equipment when upgrading then go fairly even in all the categories. The goal is to balance everything out because it will be really easy to hear the weak link when you have top tier equipment to chose from. Skimping anywhere will be heard. In this category the speakers will be slightly ahead of everything but source, amplifier and preamplifier all should be split as evenly as possible.

Difficult to drive speakers require quality amplification so go heavy there.
Lastly if the speakers you chose are extremely detailed then go heavy on the preamplifier and source.
Of course this is my opinion and how I went about thinking through my upgrade path and it worked well for me.

Wow

IMO, From most to least important:

1. Budget
2. Room
3. Speakers
4. Amplification 
5. Sources
6. Cables
7. Rack

 I've never built any system in nearly thirty years with a set percentage of budget for any particular element in chain. I've always started out with amp/loudspeaker as package deal, whatever loudspeaker I started out with required certain type of amplification, I purchase the best I can afford at this point. Rest of system follows from here.
Certainly, there is a certain percentage attached to each element at any single moment in time, just don't pay attention as I'm building system. I can only say that every single link in chain is important, when weak link discovered, 100% of my efforts and budget goes toward eliminating that weak link.

I'll preface my statement with, I don't believe in absolutes in audio, because all rooms/systems are different. That being said, I recently changed from my Jeff Rowland 625 S2 amplifier to a pair of Jeff Rowland 735 mono-amps. My dealer(Albert at Precision Audio and Video) has stated for years that, "I never really heard my speakers and he recommended upgrading my amplifier." To say the amplifiers made a difference would be an understatement. My wife never comments when I change components. Her comments, "voices and instruments have more depth." I used REL G1 mkII subs with the JR 625 S2. I sold my REL G1 mkII subs. I prefer the sound of my system with the 735s, without the G1s compare to the sound of my system with the 625 S2 amplifier and G1s. So, in my case changing amplifiers made a significant difference.