Which has greatest influence?

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.

I would say the amp/speaker match is the most critical, get that wrong it doesn't matter. Get that right and most decent preamps and sources will be ok, and only better as you upgrade, but nothing will ruin things faster than an amp and speaker that do play well toghether IMHO.