In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states—isotropic nonpure Gaussian states—we show that squeezing is not only necessary but sufficient to achieve metrological advantage. We interpret our results in the framework of resource theory and discuss possible sources of advantage other than squeezing. Our work is a step towards using phase estimation with pure and mixed states to define and quantify nonclassicality. This work is complementary with studies that defines nonclassicality using quadrature displacement estimation.