My experience with this is I’ve had 3 different Dac Amps DAC x6 was the first one I had which I did not have any reference to before switching over to a Schiit Magni 3+ and Schiit Modi 3e (Both give plenty of volume). On the Hifiman Edition XS using the DAC x6 the sound was very claustrophobic and warm compared to using the Schiit stack which was much wider and neutral sounding, for me this was a huge upgrade. To add to this I also tried this on a portable DAC Amp which is the DC03 Pro which soundstage sounds closer on the side but a bit sounds warmer. What’s your experience?
The most honest answer is “not really, no.” Obviously tubes and R2R stuff exist, but overall, modern amps and DACs all sound the same.
Some amps will distort when pushed too hard, or even exhibit weird nonlinear behavior with very low impedance loads, so having a bit of headroom is helpful.
But this is all outlier edge cases. You likely wouldn’t run into it.
I’ve never heard of the DC03 or the DAC X6, so I can’t say if you’re running into those issues. But if you aren’t, it’s likely just in your head. Simply knowing what gear you’re listening to will affect your perception of what you’re hearing.