Despite having, and enjoying my pretty high end headphone and amp system (Grado GS3000, Astell and Kern amp, about $3500 combined), they will never, to me, sound as good as my full system.
They lack the visceral impact of my full system, which is a big part of what connects me, emotionally, to the music. In essence, the difference is loading my 1,600 cubic foot room with sound pressure, compared to the .122047 cubic inches of my ear canal.
Also, when I see live music, the musicians are in front of me, and their individual positions within the acoustic space they are inhabiting, is defined in front of me. Not coming from within my head.