The relative entropies of two substances at a temperature $T'$ are not determined by their relative heat capacities at $T'$. Rather,
$$\text {Absolute entropy at } T' \equiv S(T') =\Delta S_{0 \rightarrow T'}$$
$$= \int_{0}^{T'}\frac{\text{đ}q_{rev}}{T} = \int_{0}^{T'}\frac{C_p(T)}{T} dT.$$
I.e., for each substance, you need to consider how $C_p(T)$ varies with $T$ from $T=0$ to $T=T'$. Just because the heat capacities are about the same at $T'$ doesn't mean they won't be different between $T=0$ and $T=T'$.
Intutively, the way to think about this is that the entropy is determined by how the energy levels are populated; $\frac{C_p(T)}{T}$ at any given temperature tells us the ways in which the existing populations are able to change as the temperature is increased; and the integral of $\frac{C_p(T)}{T}$ gives us the entropy by summing up these changes.
In addition, hydrogen and deuterium have different freezing and boiling points. Thus they will not always be of the same phase. This will cause further differences between their heat capacities.
To get an idea of the complexities involved in determining the relative heat capacities of these substances at lower temperatures, take a look at these two NIST publications, which give the equations of state for hydrogen and deuterium, respectively:
https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=832374
and
https://www.nist.gov/system/files/documents/2018/03/12/2fundamental_equation_of_state_for_deuterium.pdf