The short version: the mastering quality makes a huge difference.
A bit more: Audio Engineering/Production is a skill, and it’s equally important as the quality of the recording gear. The microphones were appropriately placed, the different instruments were carefully mixed and edited to make really good use of the dynamic range of quiet and loud volume extremes, and much effort throughout the process was made to keep the recording very clean. Some tracks, albums, and sometimes it seems whole genres are intentionally softened and over-processed to gloss over imperfections or to sound further away from someone singing in a moderately sized empty room. You may have heard of the “Loudness Wars,” and the (volume) compression used in that engineering decision has a large effect on that sense of liveliness and subtlety.
Some other examples of really well mastered “Headphone Food:” ‘Aja‘ by Steely Dan, ‘Graceland’ by Paul Simon, ‘Dark Side of the Moon’ by Pink Floyd, ‘Roadhouses and Automobiles’ by Chris Jones (the CD album, not just the song that appears on the ‘Smoke and Noise’ album), ‘2001’ by Dr. Dre, ‘Random Access Memories’ by Daft Punk... of course the list goes on and on, but I just wanted to drop a few samples :)