Amp vs Preamp

The Math used for matching is only that 'Math' it is not end sound.

End Sound is the result of how Upstream Electronics have processed a Source Signal, which is being transferred to a Speakers Xover, from where a conversion from electrical energy is to become mechanical energy and hence Sound is produced. 

I guestimate 99% of individuals with a keenness to experience recorded music through audio equipment, are assessing perceived quality, through the end sound they are exposed to. 

OP

Both. A lesser preamp can limit otherwise stellar amps, and a great preamp can help a bit (but not fix) a lesser amplifier. I've recently upgraded my preamp (Aric Audio Motherlode XL), and 2 amplifiers (CODA S5.5 and Aric Audio Transcend "Push Pull".

As individual components each FAR exceeded my expectations, but driving the S5.5 and Transcend with the Motherlode XL was much more than the sum of the parts.....more of a 1 + 1 + 1 = 5 type scenario, which I've never been able to experience in my own systems.

What did you upgrade to?

I would say it depends on your budget. In the low end, amps make a bigger difference - with decent, quality preamps of course, not just anything. All in the $100-500 range.

To use a analogy (a horrible one 😂 stop reading here)

the preamp gives you a tennis ball, you hit it with a racket which is the amp, and your arm is the speaker, it will fly with the force you give it.

If your racket is full of holes, you can hit the prettiest tennisball as good as a pro, it will still spin off the course.

Sorry for my goofy mood today, I must be high on the stuff coming out from the news

I'd give the edge to preamp ...

So that's probably incorrect ...