Which has greatest influence?

There are great amplifiers and great preamps. If I had only one choice it would be the preamp FWIW.

Actually it's neither,look to your source that's where it all begins.

The amp/speaker interface is the most important interface (or matching) in your system, right up there with matching cartridges and arms on a TT set up. But once you get that down, the weakest link in the chain saying applies.

FWIW, if I were starting out fresh, or all over, the first component I would buy would be the 'best' pre-amp I could afford and build my system around it. That said, if I were buying new speakers for what ever reason, I would always assume I might need to buy a different amp, just as if I were to buy a new cartridge I might have to get a different tone arm or phono stage.

Just my 2 cents.

Switiching to a tube Pre-amp gave me the most satisfying change in my system. This particular component was the first major upgrade in my starter audiophile system after reading lots of replies to a similar question from earlier forums.

All things equal, given only one choice, I'd get a better pre-amp first.