I'm thinking in terms of image quality that can't be fixed later with a program's adjustment tools. All raw converters can't be equal, some must produce better demosaic results. I would think that the amount of detail extracted from the raw file would be a part of that. Perhaps there are others I'm overlooking?
Raw converters do a number of menial tasks and a couple of critical ones, the rest is just pre-editing (you can read about a simplified breakdown of the key steps involved in rendering a raw file
here). What's critical today?
My opinion is that in late 2016 demosaicing is no longer critical: algorithms are tried, tested and stable - and they have been so for at least the last 5+ years or so, each with their known strengths and weaknesses. Improvements have slowed to the point of being almost unnoticeable from year to year. Same with sharpening and noise reduction.
Where I think they differentiate today is 1) a pleasing starting point upon first opening of the raw file, and 2) ease of squeezing camera DR into output device DR naturally. Both of these features are very subjective but, subjectively, some do better than others. They have mainly to do with getting color and (global, local, micro) contrast rendition in the desired ballpark out of the box. Pretty well everything else can be done better and more easily in a good editor like PS.
Jack