Perhaps not better ears, but probably actively looking for a distinctive quality that can be found in Paula's audio reproduction...
Her hardware does colour the audio quite a bit, and I like to use her for 8bit sample play back (though I prefer record the audio samples on my Mac with it's 24bit FireWire audio box, to ensure a clean recording).
All the old Samplers were quite distinctive, which is why I still use my Roland W-30 for all 12bit work
Well, as far as Paula goes, there was also the added link in the chain of a variety of parallel port, 8-bit samplers. These add their own colour to the mixture.
Even still, to my ears my 8 bit sample collection, some of which I sampled myself, some of which I didn't and some of which probably wasn't even recorded via Paula, sounded very similar when played back via different hardware to what it did on my Amiga.
I know there will be certain, specific sounds which are audibly different when played back via Paula than other 8-bit chips but my ears have never noticed this to any degree where I could say with certainty that I preferred the Paula version. This is despite around a decade of pretty-much-daily sampling and recording on the A1200.
I should also add that I can't tell the difference between a 320kbps mp3 and a 16 bit .wav either. However, there were a couple of youngsters on my sound engineering course who claimed they could. So, in my case, I think it *is* my ears (or at least how I perceive what they hear).
In such circumstances the pursuit of said, unique sounds would take me into a spiral of diminishing returns that I'm far too old to devote the time too.