You have received some insightful comments to your question.
My experiences mirror @mikelavigne (i.e., "most dacs are decent"), @czarivey's comments on "voltage output", and @ghdprentice regarding the presence of "distortion and high frequency trash".
Of the better DACs I have owned and/or auditioned for a time in my own system, they all sounded mostly "acceptable" yet there were indeed differences that in my world typically lean toward the perception of either greater resolution or tonal density. I don't care for what some may characterize as "warmth," as I believe that indicates clouded clarity, probably resulting from distortion. I want clarity that a high S/N provides, but the absence of tonal density and dynamics/impact are deal-breakers for me. I do believe you can mostly have both but you may need to settle just a little on one side or the other and, if the DAC sounds good, you will likely forget about those nuances after owning it for a while. The DACs I like seem to display a rich tonal density and dynamics/power fully across the volume range, i.e., you don't have to chase the volume control to achieve impact and tonal color. My goals are more about getting the midrange and bass right, but the high frequencies need to sound natural without roughness caused by "distortion and high frequency trash" . Clearly, the rest of the system needs to be able to keep up.
IME, there are certainly audible differences that you can notice upon first listening to different DACs. However, in many cases with better DACs, the differences may be subtle so you may need to listen for a while and do some A/B comparisons to pinpoint exactly what the differences are and how they affect your listening enjoyment.