  Mixed valence spinels provide a fertile playground for the interplay between
charge, spin, and orbital degrees of freedom in strongly correlated electrons
on a geometrically frustrated lattice. Among them, AlV$_2$O$_4$ and
LiV$_2$O$_4$ exhibit contrasting and puzzling behavior: self-organization of
seven-site clusters and heavy fermion behavior. We theoretically perform a
comparative study of charge-spin-orbital fluctuations in these two compounds,
on the basis of the multiband Hubbard models constructed by using the
maximally-localized Wannier functions obtained from the ab initio band
calculations. Performing the eigenmode analysis of the generalized
susceptibility, we find that, in AlV$_2$O$_4$, the relevant fluctuation appears
in the charge sector in $\sigma$-bonding type orbitals. In contrast, in
LiV$_2$O$_4$, optical-type spin fluctuations in the $a_{\rm 1g}$ orbital are
enhanced at an incommensurate wave number at low temperature. Implications from
the comparative study are discussed for the contrasting behavior, including the
metal-insulator transition under pressure in LiV$_2$O$_4$.
