Which has a greater influence on sound quality, the amp or the preamp?

Someone noted above that the efficiency of the speakers makes a major difference. It seems to me that, mathematically, if the speakers are very efficient, then the output is more a function of the preamp, let’s say 70/30 for the preamp, and if they are quite inefficient, then the output is more dependent on the power amp, say 30/70 for the main amp. Also, whichever amp is being driven higher/harder will, especially if it breaks into some mild distortion of even harmonics, will color the sound more, either warming it with richness or detailing it with presence, depending on the tubes in each amp, whether they are complementary or contradictory, and which amps are having the greatest influence. And this same influence may have an effect on SS amps as well, depending especially on the output chips selected vs. the power chips.  

And someone above alluded to garbage in, garbage out when impressing on the importance of the pre-amp. True. And the most we can control if our source is streaming or CD. But, that applies to the earliest point in the system we can control, and we still see a lot of people not paying attention to their cartridge and stylus on their turntable - the ultimate GIGO. (We are hoping the producers of any records-CDs are recording to highest standards and pressing the vinyl right, etc.)  Just sayin. 

I try not to use a component that’s obviously colored ahead of the power amps. Get a good transparent source and a good transparent preamp, then you can indulge yourself and shape the presentation a little with your choice of power amp, knowing that everything upstream is as true to the source as your budget constraints allow.

Probably the phono stage, the preamp, and the power amp; in that order. Best of the are all pure tube.