I've always heard (and believed) that tubes sound as good as they do for 2 primary reasons:
1 - They better convey the particular harmonic structure of notes from different instruments (accuracy of tone & timbre)
2 - And very often, they overload more gracefully/less abruptly than SS devices, and the distortion byproducts sound more benign (the distortion representing more even-order harmonics and fewer odd-order ones).
But that doesn't really explain the 3D effect one often gets from tubes, where each musical note sounds more tangible, real, occupying real space in a real place. For me, that is the greatest asset of tube audio: how musically realistic the sound is.