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

I’m not an engineer, but my uneducated guess is that the harder the speaker is to drive the more the amp matters in terms of sound quality.  My speakers are a relatively easy load and I hear bigger differences between preamps than amps, which would echo what others have said that “it depends.”  In the end, and no matter which one makes a bigger difference in a given system, balance is the key and that the amp and pre compliment each other in ultimately achieving the desired sonic characteristics.  That’s my take/experience anyway.

Both!!!

@inna +10!

It really depends on how neutral and transparent each piece in question is. In a top notch system, the weakest link will stick out like a sore thumb...not so much on a system with multiple veiling and smearing issues. Plus, as mentioned, the amp/speaker interface matters.

At some level everything matters.