Amp vs Preamp

 I suppose it might be easier to stay within the same lineage or company when trying to match the components. 

I think you'd be less likely to get a truly awful combination that way.  But that typed, I know that there are a bunch of members who report sublime sound by mixing & matching.  

@mpomerantz you match sensitivity of an amplifier to the output voltage of preamp and you match output impedance of your preamp to input impedance of poweramp.

There are also vendors that provide home trials. The preamp I use does that, the Benchmark HPA4. 

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.