Linker histones are epigentic regulators that bind to nucleosomes and alter chromatin structures and dynamics. Biophysical studies have revealed two binding modes in the linker histone/nucleosome complex, the chromatosome, where the linker histone is either centered on or askew from the dyad axis. Each has been posited to have distinct effects on chromatin, however the molecular and thermodynamic mechanisms that drive them and their dependence on linker histone compositions remain poorly understood. We present molecular dynamics simulations of chromatosomes with two linker histone isoforms, globular H1 (GH1) and H5 (GH5), to determine how their differences influence chromatosome structures, energetics, and dynamics.Results show that both linker histones adopt a single compact conformation in solution. Upon binding, DNA flexibility is reduced and there is increased chromatosome compaction. While both isoforms favor on-dyad binding, the enthalpic benefit is significantly higher for GH5. This suggests that GH5 is more capable of overcoming the large entropic reduction required for on-dyad binding than GH1, which helps rationalize experiments that have consistently demonstrated GH5 in on-dyad states but that show GH1 in both locations.These simulations highlights the thermodynamic basis for different linker histone binding motifs, and details their physical and chemical effects on chromatosomes.