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

Both!!!

Yeah, balance is the key. And speaking of tube equipment - tubes matter, a lot.

@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.

Each are important but a high quality, low noise high gain preamp can bring your system to a higher level of excitement and dynamics than a basic preamp connected to a powerhouse amp.