The translation of the CG, which is at the geometric center for both spheres, is governed by ${\bf F} = m {\bf a}$, where ${\bf a}$ tracks the CG. You might say that since both spheres have the same mass, they will translate in the same way, but ${\bf F}$ becomes different for each sphere as time evolves.
If you attach a unit tangent vector ${\bf e}_t$ to the rim of the sphere, then ${\bf F}$ may be represented as ${\bf F} = F {\bf e}_t$. $F$ is the same for either sphere, but the evolution of ${\bf e}_t$ will depend on how quickly each sphere rotates. The sphere with the higher moment of inertia, for example, will rotate slower, and so ${\bf F}$ will spend more time initially vertical than in the case of the other sphere.
Therefore, the translation is different for each sphere.