The Generalized Feistel Network (GFN) has long served as a versatile foundation for lightweight block cipher design, with the even-odd shuffle variant offering particularly strong diffusion properties. Recently, MGFN was introduced under Malaysia’s National Cryptography Policy, followed by MGFN-P, which replaces the original S-box with that of PRESENT to enhance resistance against differential attacks. In this work, we present a comparative study of MGFN, MGFN-P, and TWINE to reassess the root causes of MGFN’s cryptanalytic weaknesses. Our analysis shows that these weaknesses cannot be attributed solely to the low branch number of MGFN’s S-box, but arise primarily from the structural permutations used in its design. To investigate whether security can be improved through alternative permutations while fixing the S-box, we evaluate MGFN variants under both nibble-wise and bit-wise permutations. By exploiting equivalence relations, we reduce 40320 nibble-wise candidates to only 22 equivalence classes and identify variants with stronger resistance than MGFN and MGFN-P, though still weaker than TWINE. In the bit-wise setting, exploratory experiments with cyclic shifts and random permutations yield stronger variants, but none match TWINE’s robustness. Overall, our results underscore the limitations of MGFN’s design and reaffirm the reliability of well-established GFN configurations for lightweight cryptography.