We analyze design principles of transcription factor (TF) recognition by genomic DNA in differentiating human embryonic stem cells for 36 TFs and five histone modifications in four developmental layers, using the data recently measured by Tsankov et al. This analysis reveals that DNA sequence repeat symmetry plays a central role in defining TF-DNA binding preferences across different developmental layers. In particular, we find that different TFs bind similar symmetry patterns within a given developmental layer. While the TF cluster content undergoes modifications upon transitions between different developmental layers, most TFs possess dominant preferences for similar DNA repeat symmetry types. Histone modifications also exhibit strong preferences for similar DNA repeat symmetry patterns, with the symmetry strength differentiating between different histone modifications. Overall, our findings show that despite the enormous sequence complexity of the TF-DNA binding landscape in differentiating human embryonic stem cells, this landscape can be quantitatively characterized in simple terms, using the notion of DNA sequence repeat symmetry.