Seems like the silicon atom is more oxophilic as compared to the phosphorus atom. This could in principal be explained by the higher strength of the $\mathrm{Si-O}$ bond, as indicated by the dissociation energies $D$ (see http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html):
$$
 \mathrm{Si-O}:~~~~D=\mathrm{452~kJ/mol};~~~~r_b=163~\mathrm{pm}
$$

$$
\mathrm{P-O}:~~~~D=\mathrm{335~kJ/mol};~~~~r_b=\mathrm{163~pm}
$$
The $\mathrm{Si-O}$ bond is stronger thus given an explanation why the Peterson olefination is favoured.
It seems that the bond lengths $r_b$ are the same, though.

By the way, a nice discussion of oxophilicity was given recently in _Inorg. Chem._, **2016**, _55_ (18), 9461.