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

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. 

Both of course, but to answer the question I agree with ghdprentice.

Either preamplifier or amplifier can dramatically improve or worsen the sound of your system.  However, since there are plenty of good amplifiers in comparison to not so many good preamplifiers, my vote goes to - Preamplifier.