Most modern converters are very good - even the cheap ones. The chips inside are mostly the same, although the other analog components are better and worse - which seems to have as much to do w/ longevity of the unit as sound.
Many moons ago I was disappointed when I switched from a Presonus Firepod to a TC Konnket. Of course, as above, I was also listening through the pres, too (comparing acoustic recordings). There was a difference, but small, and I assume a lot of that was the better pres. I assumed there should be an obvious difference that would jump out - "like a veil was lifted" sentiment.
Later when I stepped up to TASCAM UH-7000s I could hear a difference or maybe as one gets older one's hearing gets better (or you just learn what to listen for?). I was brighter - which isn't always a great thing - on some old-style songs the darker presonus sounded better since it better fit a low fi, old style music (or it didn't bother me). And there is littler difference between the 7000 and the TASCAM US series.
Converters would be the last thing I'd worry about, unless I had the extra funds for a Burl or other top notch converter. Even then that would be more of a marketing (or feel-good-about-yourself) thing than actual music making.