Average kinetic energy per molecule per degree of freedom $=\frac{1}{2}kT$. Since, both the gases are diatomic and at the same temperature $\left(300 \mathrm{K}\right)$, both will have the same number of rotational degree of freedom i.e., two. Therefore, both the gases will have the same average rotational kinetic energy per molecule $=2\times \frac{1}{2}kT=kT$. Thus, ratio will be $1:1$.