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For one of my system i calculate i get the following values in which the TOTEN and energy (sigma->0) are the same .
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FREE ENERGIE OF THE ION-ELECTRON SYSTEM (eV)
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free energy TOTEN = -719.360085 eV
energy without entropy= -719.360085 eV energy(sigma->0) = -719.360085
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But for few of other systems, i see difference in the three values as below.

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FREE ENERGIE OF THE ION-ELECTRON SYSTEM (eV)
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free energy TOTEN = -919.772568 eV

energy without entropy= -919.763224 energy(sigma->0) = -919.767896

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Therefore i wish to ask you which energy should i consider for the Total energy for comparing it with the other structure with similar composition.

You should use 'energy(sigma->0)'.
If both energies are the same it means that there was no effective smearing, because eg. the band gap was large. In the other case you have partially occupied unoccopied states caused by smearing, which is actually a numerical trick to get better convergence. This yields additional entropy, which is _not_ in the system at this point. So that's why there is this correction.

Cheers,

Alex