The energy transfer, dissociations, and chemical reactions between O2 and N2 play an important role in the re-entry process of aircraft and many atmospheric, combustion, and plasma processes. Recently, Varga et al. (J. Chem. Phys., 2016, 144, 024310) developed a full-dimensional high-precision potential energy surface (PES) of the ground triplet electronic state for the O2 and N2 system based on ca. 55,000 data points, whose energies were calculated by multi-state complete-active-space second-order perturbation theory/minimally augmented correlation-consistent polarized valence triple-zeta electronic structure calculations plus dynamically scaled external correlation. The fitting function adopted the many-body expansion form with the four-body interactions fitted by the permutationally invariant polynomial in terms of bond-order functions of the six interatomic distances (MB-PIP). In this work, we refit the PES of the N2O2 system by two methods based on the same data set that was used by Varga et al. The first uses the permutation invariant polynomial-neural network (PIP-NN) method to fit the entire energy of the 55,000 data points. In the second approach, the PIP-NN method is used to fit only the four-body interaction component, a similar treatment in the MB-PIP method, and the resulting PES is named MB-PIP-NN. Then, the performances of these new PESs and the MB-PIP PES are comprehensively and systematically compared, such as comparisons of various scans, properties of stationary points, and dynamics simulations. Possible improvements for the PES of N2O2 are suggested. A more reliable PES of the system can be constructed in terms of data sampling range, electronic structure calculation level, and fitting method for high-temperature calculation and simulation in the future.