Longtime vinyl lover here--someone who successfully transitioned to digital-only in the desktop audio setting (including quality headphones--very revealing of digital). A few observations:
1 - The trad way to get better sounding digital is to throw extreme money at delta-sigma conversion chips. Things like intricately designed input sections; big power supplies; heavyweight output sections; and sometimes, exotic bit-shaping circuitry in the digital section (ie, not defaulting to stock filter options of the chip itself. I haven't heard any of these dreadnaughts, which can cost upwards of $20K-$30K, but trust the comments I read that these DACs are a glimpse of sonic heaven.
2 - But back in the real world, I found one needn't spend so much or work nearly so hard to get better digital sound. I'll echo what teo_audio said about R2R & ladder DACs. Yes, it's an old technology and requires precise resistor matching (if a true ladder is used); or absent that, a very well conceived & programmed FPGA section. But these types of DACs sound far less "digital" than anything I've yet heard.
3 - In my experience, the NOS (non-oversampling) variant of R2R & ladder DACs is best for me. The sound is simply more organic, relaxing, suggestive of recording space, and representative of actual, 3-dimentional instruments (which produce 3D notes). Not all NOS DACs are amazing--these designs have to be very carefully planned & executed w/quality parts. But that's a given in any audio sphere.
My 1st non-D/S DAC was the humble NOS 19 by the well-known Chinese audio designer/mfr, Audio GD. It completely transformed my relationship w/digital. For the first time, I could relax and hear music coming from this DAC. I got interested in Audio GD and decided to buy their biggest selling DAC ever, the resistor ladder DAC-19. It, too, is very fine-sounding digital.
I since sold the NOS 19 & replaced it with an NOS DAC I got interested in, the MHDT Labs Orchid. It, too, offers very humane, musical sound. I just swapped out the stock tube from the buffer circuit for a highly-recommended NOS variant. Even w/o the tube being fully burned in, it already sounds rather amazing.
