The degenerate fundamental mode of a microcavity pillar structure with circular cross section splits into two linearly polarized modes when the shape is changed to elliptical. The quality factor Q of these modes is very different. This letter demonstrates that the high Q mode provides better values of the figure of merit for strong coupling applications, Q∕V), where V is the modal volume, compared to values obtainable in circular structures. The difference in Q is shown to be a consequence of the polarization dependence of the losses through the microcavity mirrors.