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

....and all 'n all, it's just synergy, y'all.....

That, and your preferred POV.... ;)

They both offer different sound quality and sound characteristics.  

"Is it the inside dirt or the outside dirt that matters most?" assumes a nonexistent hierarchy.  It's the side of the glass with the most dirt tempered by whether fingerprints or water spots bother you more tempered by what floor you are on and how tall is your ladder.

The CLOSEST you get to a LIVE performance with a Wide and Deep soundstage is with a Tube preamp and a Solid State amp. Period.

@mbmi I get all of that using my passive (battery powered for pitch black backgrounds) with a tube phono stage and SS amps.