I know what you mean! Sounds like your headset was not properly driven without amp.

I just did similar experiments with my non-audiophile friend (because he was curious why I need an amp, haha). We compared the same song on the same headphone (AKG K712) with nfb11.38 dac/amp vs without amp. My non-audiophile friend described that without amp, it was like looking at a 2D photograph of a 3D object.

The separation becomes clear on a song with very low and very high frequencies --- try Billie Eilish - bad guy.