We argue that the large Jahn-Teller (JT) distortions in YVO3 and LaVO3 should suppress the quantum orbital fluctuation. The unusual magnetic properties can be well explained based on local density approximation + Hubbard U calculations using experimental structures, in terms of the JT orbital. The observed splitting of the spin-wave dispersions for YVO3 in a C-type antiferromagnetic state is attributed to the inequivalent VO2 layers in the crystal structure, instead of the "orbital-Peierls state." Alternative stacking of ab-plane exchange couplings produces the c-axis spin-wave splitting; thus, the spin system is highly three dimensional rather than quasi-one-dimensional. Similar splitting is also predicted for LaVO3, although it is weak.