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

Well, sound preferences differ, so do preamps. As far as I know, most audiophiles do have active preamp in their systems. Going direct can give more pure but less refined presentation.

@inna Yes, I agree most do, but that doesn`t mean much really.

Can you explain the "less refined presentation" part ?

I’m of the camp of “the entire audio chain matters”.  It’s not pre vs amp, but rather work on the weak links in one’s audio chain 

Signal source. Garbage In, Garbage Out.

Would have to agree with signal source being the most palpable. An upgrade of streamer with a good power supply (and better power cable on it) pretty well transformed my system.