Benzene is less reactive than we would predict from the kekule structure. Its bonding is therefore stronger and requires more energy to break.
Are we talking about hydrogenation? If so, the same amount of energy is given out by forming 6 x C-H bonds in both cases to give the same energy:
Benzene (kekule) + 3H2 -----> Cyclohexane: Enthalpy change = 3(C=C)+3(H-H) broken + 6(C-H) formed = X - [6 x 413] = -360
Benzene (actual) + 3H2 ------> Cyclohexane: Enthalpy change = aromatic ring broken+3(H-H) + 6(C-H) formed = Y - [6 x 413] = -208 = less energy given out to make the same thing
This means that Y > X i.e. it takes more energy to break the aromatic ring than the 3 double bonds