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

The CLOSEST you get to a LIVE performance with a Wide and Deep soundstage is with a Tube preamp and a Solid State amp. Period.

@mbmi I get all of that using my passive (battery powered for pitch black backgrounds) with a tube phono stage and SS amps. 

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!