Instabilities in vectorial Kerr cavities can arise from two different bifur
cations of scalar and vectorial character. We study the conditions that det
ermine which of the instabilities is responsible for pattern formation. We
find that a subcritical homogeneous polarization instability governs patter
n formation when cavity anisotropy or injected field detuning is large. Und
er these conditions the system exhibits bright cavity solitons.