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

Yes, the preamp is the heart of the system.

But I have always felt that the “2 hands clapping” are the speakers and the amp.

The contribution of the preamp is more subtitle and surely subtitles are central.

But, IMO, the “broad strokes” belong to the amp and speakers.

I used to be in the anti-preamp camp for a long long time. I had evidence that preamps don't matter at all, they make zero difference. At least I couldn't hear it. Until one day, I got one and plugged it in. 

I am still kicking myself for selling a Rogue Rp7 pre w/ top of the line NOS tubes.

I have a well regarded SS integrated now but definetly lost a little magic.