Color difference among oxovanadium species
The colour will depend on several factors. You've identified the oxidation state (+5 in both cases) as one.
Other factors are:


Ligands
Complex shape


With $\ce{[VO2]}^{+}$, the actual complex ion is $\ce{[VO2(H2O)4]}^{+}$ (Taken from ChemGuide). So our ligand is water, and the shape is tetrahedral (or square-planar).

The $\ce{[VO4]^{3-}}$ ion usually only exists at high pH in solution but polymerises at lower pHs. These polymeric ions can have colour (e.g. $\ce{[V10O28]^{6-}}$ is orange).(Link for colour / polymerisation)
However, I could find no details as to the ligands (I would assume that they would be hydroxide ions at high pH) nor shape.

If we are talking about the solid, then the same applies... does the solid have any water of crystallisation. (Think copper sulfate... blue when "wet" and white when "dry").