This work presents an experimental study of the network structure of swollen, charged hydrogels. We provide an in-depth comparison of two proton low-field NMR methods, i.e., transverse relaxation and double quantum spectroscopy, that are both sensitive to residual orientation correlations of the network chain segments. The results are in both cases analyzed by help of integral inversion techniques, and both methods are demonstrated to provide comparable results despite the more qualitative nature of the transverse relaxation. We investigate model samples that are similar to commercial superabsorber materials based on partly neutralized and chemically cross-linked poly(acrylic acid) as prepared by free radical polymerization. The degree of cross-linking and the monomer concentration are varied during synthesis. Both parameters are found to affect the network structure and the amount of elastically inactive defects in a systematic way, and a comparison with commercial samples with homogeneous or purposely inhomogeneous core-shell structures proves that the cross-linking bimodality of the latter is readily revealed despite the rather large intrinsic inhomogeneity of the swollen gels.