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

I am pretty sure this identical question has been asked in the past, and every time I have read it, the answers are (like almost all audio topics here) split with no clear consensus, and a lot of "both" answers.

I am going with "both," but the importance of each manifests itself in different ways. I’ve played around with a few different tube amps, and each amp change did something. I didn’t start to feel like my system was sounding truly "musical" until I upgraded from a digital HT preamp to my first tubed preamp. I upgraded that to a better tubed preamp and lost some warmth but gained air and detail (which to me means a better imaging and a better defined sound stage).

The answer is always the same, it depends. That said it's hard to beat a great tubed preamp.

Whichever, in the current setup, is less good.

It is probably impossible to beat a great tube 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.