What is the relationship between entropy and heat capacity?

The molar heat capacity of hydrogen gas and deuterium gas are nearly the same, $\pu{28.8 J K-1 mol-1}$ and $\pu{29.2 J K-1 mol-1}$, respectively, but the absolute entropy of deuterium ($\pu{145.0 J K-1 mol-1}$) is significantly larger than that of hydrogen ($\pu{130.7 J K-1 mol-1}$).

I have seen the equation that associates the heat capacity to entropy, and I understand the equipartition theorem and different modes of motion contribute to the heat capacities. Since the heat capacities are fairly the same, what other factors can affect the entropy in these species?