An audiophile DAC goes well beyond just getting the major sounds right. It is highly refined. So the thsss of a drumstick hitting a cymbal sounds like brass. the highly complex sound of a trumpet or sax has the full complexity for a brass instrument not just a cartoonish impression. The human voice becomes fully fleshed out. Very often on budget equipment, Schiit being a good example, the voice is recognizable but thin and a bit week... heard through a really good DAC it has real serious midrange weight.. I am not a fan of Tony Bennett and Frank Sinatra.... but the difference through a great DAC (with appropriate associated equipment) is simply astonishing... the power and depth of their voices. While, they are not my cup of tea... on a great system with a great DAC you can’t help but understand why they are so famous.
Some examples of Audiophile DACs would be Berkely Alpha Reference 3, Audio Research Reference 9, dCS Bartok (although I find this a bit thin... polite as it often referred to), MSB.