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

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.

I spent 50% on speakers....  60 % on amp , 50 % on sources....