I have owned multiple DACs over the years--all connected with desktop audio, and none in the multi $1K range common in big living room audiophile setups (which I had years ago, pre-DACs).
Anyway, I have most definitely heard differences between various DACs. For example, I hear distinct, though subtle differences between multi-bit DACs and delta-sigma designs; also differences between good multi-bit and pure/non-oversampling multibit.
HOWEVER...I've also learned that when a given DAC is made very well, with robust power supply, well-implemented digital section, best available USB receiver, etc--it's harder to pick out those subtle differences when comparing to another, equally well designed & constructed DAC. If one were comparing, say, 5 top level-DACs, I'd expect the multi-bit one to diverge a bit from the others in timbre of instruments, lack of grain & glare, and a slightly "wet" (ie, non-dry), rounded sound to bass. But at the top level of design/built, differences between DACs become fairly small (unlike amps and speakers, which are all over the place).