The three-dimensional (3D) organization of interphase chromatin in eukaryotes is complex; details of the corresponding genome structures vary stochastically from cell to cell. Here, we propose a metric to quantify the cell-to-cell heterogeneity of the 3D chromatin conformations in ensembles of single cells: () is defined as the standard deviation of the ensemble distribution of the per cell average Euclidean inter-loci distances , for a given genomic separation between the loci. We have used the metric to examine and quantify in detail the cell-to-cell heterogeneity of conformations of the interphase X chromosome in fruit fly generated via three distinctly different modeling approaches, which take experimental Hi-C data as input. Two of the approaches use bulk Hi-C and lamina-DamID data, while the third relies on single-cell Hi-C maps. An algorithm is proposed to facilitate comparison of of models constructed at different resolutions, and to examine the behavior of conformational heterogeneity with increasing model resolution. Higher resolution models show a greater , in general. The impact of the model resolution is strongest near the genomic distance corresponding to the resolution limit of the model, and diminishes for larger genomic distances: extrapolating the resolution from approximately 14 kb to 2 kb has little effect on the beyond ~100 kb. All chromatin models examined in this work show a very similar trend of monotonically increasing structural heterogeneity with , up to the genomic TAD size; beyond that, significant differences arise, with the model based on single-cell Hi-C showing nearly opposite trend compared to the two models that use bulk Hi-C data. We attribute these major differences to relatively subtle differences in the modeling approaches, which we discuss. Based on the analysis, we propose to explore the possibility of inclusion of bulk Hi-C data into training of chromatin models that are based on necessarily limited single-cell Hi-C data. Within our computational approach, depletion of nuclear lamins leads to increased structural heterogeneity at nearly all genomic separations, with the potential implication that cell functions that depend on chromatin structure might be more variable within lamins depleted nuclei compared to the wild type.