The spectral characteristics of turbulence associated with the two-dimensional magnetized Rayleigh-Taylor instability in the presence of a background neutral gas are studied. Particular attention is paid to comparing the electrostatic potential spectra obtained in the ion-neutral collision-dominated case with the spectra from the ion inertia-dominated case. The time-averaged one-dimensional spectra along kx and ky for the collisional case are found to be Px∝kx-3.7¿0.3 and Py∝ky-4.6¿0.3, respectively, where x is the direction of the density gradient and gravity. Correspondingly, the spectra for the inertial case are given by Px∝kx-3.8¿0.2 and Py∝ky-3.8¿0.2. Thus the potential spectrum in the collisional case shows a marked anisotropy in contrast to that of the inertial case, which is isotropic and exhibits Kolmogorov scaling. The anisotropy in the collisional case is attributed to the frictional nature of the turbulence and the suppression of inertial overshoots. Application of these results to ionospheric turbulence is discussed.