Except the difference in approach and it is pople and it is karlsruhe basis sets. And kindly tell me how we can justify TZVP is more accurate in the sense of extra function for valence.
6-31 G is Pople's basis set which is split-valence basis set. TZVP is a Karlsruhe basis set which can be called as valence triple-zeta polarization. Pople's basis sets are considered as outdated and sometimes can lead to incorrect results (see paper "Popular theoretical methods predict benzene and arenes to be nonplanar". J. Am. Chem. Soc. 128 (29): 9342–9343). However, they can be used still and are implemented in many QC codes. I guess the result mainly depends on what you are calculating. For example, when you calculate partial charges for force fields, in my experience most of basis sets and functionals would give very similar results, but when you concern dihedral potentials then you shall take into account that the error shouldn't be more than 1 kJ/mol.
TZVP basis set include polarization functions which add some flexibility to the MO shapes and might be crucial for revealing weak interactions, density shifts, distortion of bonds and so on.
The more functions we add the lower the energy we get simply due to the variational principle. In that sense, any addition of the basis functions will get us closer to the HF limit which is usually extrapolated by CBS (complete basis set) approach. However, this impact on electron energy has nothing to do with the accuracy of basis set and suitability for a specific application.
However, my recommendation is that the basis set choice should be guided not by its size but by its credibility for specific needs. I would search for benchmarks on different systems and pick the one that performs best for your kind of systems. TZVP is usually a good choice and, for example, it is recommended for general calculations in ORCA by the authors.
So, you can use ORCA manual and any other publications to justify your choice.
Hope that helps,
Nikita.
To add to these great answers above: you can cite https://www.ncbi.nlm.nih.gov/pubmed/26605468 when talking about the superiority of TZVP versus 6-311G family. But as usually YMMV and there may be some instances where Pople's basis sets give better results and many instances where the results obtained using both basis sets are very similar.
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