During analysis of benzene we see that the bond lengths and angles are all the same. In the theoretical molecule however, due to the differing lengths of bonds between double and single bonds, the bond lengths and angles are all different.
In addition to this, calculating the theoretical enthalpy for hydrogenation of the structure yields a result of around -360kJmol-1 . Whereas, the actual value for hydrogenation of benzene is around -208kJmol-1 , around a 152kJmol-1 difference. This therefore means that the theoretical Kekule's structure is fundamentally different to the actual structure of benzene.
In the true structure of benzene, each carbon bonds to two other carbons and a hydrogen in a trigonal planar shape. This leaves a single, unpaired electron in a Pz orbital (A dumbbell shaped orbital that is perpendicular to the z-plane of the molecule). All six of the carbons in the molecule do this; which forms two rings of delocalised electrons above and below the molecule. These electrons occupy a molecular orbital that combines all 6 spare pz orbitals. This is the reason for the stable nature of benzene.