Why [FeF6]3– is colourless whereas [CoF6]3– is coloured ?

[FeF₆]^3- is a Fe (III) complex hence [Ar] 3d⁵. F^- is a weak field ligand and the complex is high spin: 

                                     t₂g (↑) (↑)(↑)   →Δ_oct→     (↑)(↑)eg.

And there is 5 unpaired electrons hence it's spin multiplicity = (2S+1) = 6  , and multiplicity of  a excited is cannot be six thus The transitions in Fe ⁺³ ion are spin forbidden and are extremely weak so as to make [FeF₆]^3- almost colorless.

[CoF₆] ^3- this is a Co (III) complex [Ar] 3d⁶. Again F^- is a weak field ligand and [CoF₆]^3- is one of only two common cmplxs that is high spin:

                       t₂g (↑↓) (↑)(↑)     →Δ_oct→      (↑)(↑) eg

Only one band is expected namely the t₂g→eg transition (d¹). The complex is blue consistent with this transition being in the low energy red.