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

If your preamp or source is lacking, it will not matter how good your amps and speakers are- they cannot make up for signal loss or coloration! The preamp has to be right!

Amplifiers tend to have the most distortion of any of the links in the electronics chain (loudspeakers tend to have even more). Because of this its important than the distortion of the amplifier be benign (lower ordered harmonics) since the "sonic signature" of any amplifier is the distortion it makes (IOW you hear distortion as tonality).

I agree with @soix . It largely depends on your speakers. If your speakers have low sensitivity along with a difficult impedance curve the amp will make a huge difference. If your speakers go down to 2 ohms or lower with a punishing phase angle then they need an amp that will double its power with each halving of the impedance. If you run these speakers with a tube amp or light duty SS amp you will get a highly distorted frequency response. Your speakers will sound weak in the frequency areas of low impedance.

I'm running a pair of Thiel CS6 speakers with a Krell KSA 300S that produced 300 watts at 8 ohms and 2400 watts at 1 ohm. My speakers present one of the most difficult amplifier loads of any speaker you can find. Certain Wilson speakers are another example of this. I've read forum comments from audiophiles who have felt that the CS6's have a lower midrange "suckout." Well, they were absolutely right! They were using a tube amplifier to drive their Thiels and that is exactly what you would expect to hear.

IMO, speaker/amplifier matching is one of the most important and most neglected areas of audio. My Krell would be completely inappropriate to drive a pair of 105 dB sensitivity horn speakers. But it is one of the few amplifiers that can achieve a flat frequency response with my Thiels.

@atmasphere wrote "you hear distortion as tonality"

Could you explain? Thanks!

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.