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

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. 

Through the Sixties through the two thousands, I had. separates ( with one exception). Everything I changed, changed the sound. I bought a Hegel integrated a couple of years ago and it’s great, but early this year, I went back to separates and I’ve been having a blast rolling tubes again.  And yes, tubes make a difference as well.