I will agree with everybody at the same time.
The order of importance for a track is:
#1 the performance/material
#2 the instrument (same as #1 in the case of vocals)
#3 how the track is mixed, skill of the engineer.
#4 The mic placement (A well placed SM57 is better than a poorly placed U87)
#5 the Mic choice, There is a right place for Dynamic, Condenser , and Ribbon, plus Large and small of each.
#6 The preamp, A bad one and really take the life out of a track
#7 The converters. Bad clocking/converters really adds nasty distortion.
I read a comment I will never forget. "It's amazing how much a singer sound like themselves through any microphone"
With the converters down at the bottom of the list, everything else is more important. Back in the late 90's I had two different sets of converters. ADAT's had 18 bit converters built in, and I had a V8 Big block. The big block was only 16 bit, but man did it sound great vs the ADAT's converters.
With low track counts (say 12 and under), the high end converters will not make much of a change. Once you start getting to 32+ tracks and looping stuff out/in for using analog gear, then good converters help preserve the quality of everything going on. If you like fighting word clocking with multiple converters (I hate that game) I actually think a mix turns out best when a mixture of converters are used. This is just like using a mixture of preamps and Mics. If I record 24 tracks using all U87's and Neve preamps, the mix will not turn out as well vs using a mixture of U87's, SM57's and 58's with a ribbon and 421 in there recorded through a wide selection of cheaper preamps.
I like to vary the sources input chains as much as practical.....key word....practical. Different sources blend together easier. This includes the converters as they do add a sonic signature like any piece of Audio gear.
I identified this with my first decent tube mic, The Groove tube MDa1. The mic sounds great for a single track. Try to use that mic for multiple track say vocals and guitar, the two tracks will fight each other for the same sonic space forcing one to EQ them differently just so they can co-exist. Once I found that out, I experimented and found that any variance you can practically create helps the blend when it's all done.