I haven't heard or owned a lot of DAC's, but have owned California Audio, Cambridge, Theta Digital, Schiit Yggy, and Cary. Of those, the Cary DMS-700 was by far my favorite. It uses the AKM AK4499EQ in conjunction with a FPGA chip and find it to be very analog sounding. I have no inclination to change for a long time.
AKM makes the best DACs
OK, before you flame a reply to my heading please read this section.
It is a terrible idea to judge a DAC based on the chip. I don't think consumer's should ever do that. I think there is a lot that goes into a good external DAC unit and the converter chip is just one of many factors that go into the final sound.
Having said that, it turns out I tend to like the sound of DACs with AKM chips over most others. A long time ago I would have said the same about Burr Brown.
For converters which use an all in one chip what is the brand you find yourfself more likely to like the sound of vs. not?