In the last decade, several experimental studies have shown how chromatin modifications (histone modifications and DNA methylation) and their effect on DNA compaction have a critical effect on cellular reprogramming, i.e., the conversion of differentiated cells to a pluripotent state. In this paper, we compare three reprogramming approaches that have been considered in the literature: (a) prefixed overexpression of transcription factors (TFs) alone (Oct4), (b) prefixed overexpression of Oct4 and DNA methylation "eraser" TET, and (c) prefixed overexpression of Oct4 and H3K9me3 eraser JMJD2. To this end, we develop a model of the pluritpotency gene regulatory network, that includes, for each gene, a circuit recently published encapsulating the main interactions among chromatin modifications and their effect on gene expression. We then conduct a computational study to evaluate, for each reprogramming approach, latency and variability. Our results show a faster and less stochastic reprogramming process when also eraser enzymes are overexpressed, consistent with previous experimental data. However, TET overexpression leads to a faster and more efficient reprogramming compared to JMJD2 overexpression when the recruitment of DNA methylation by H3K9me3 is weak and the MBD protein level is sufficiently low such that it does not hamper TET binding to methylated DNA. The model developed here provides a mechanistic understanding of the outcomes of former experimental studies and is also a tool for the development of optimized reprogramming approaches that combine TF overexpression with modifiers of chromatin state.