We present a symmetric double-sided pillared phononic crystal (PPnC) where either quantum spin Hall effect (QSHE) or quantum valley Hall effect (QVHE) is emulated by solely imposing different perturbations to the geometry. When occurring at the deep subwavelength scale, the valley-polarized edge state emulating QVHE becomes evanescent at the zigzag termination and can be enhanced by a locally resonant mode. When occurring at high frequency, the refracted patterns (refracted modes and angles) can be tailored. Furthermore, we demonstrate the occurrence of the pseudospin and pseudospin-valley combined edge states and the valley-dependent propagation at a T-junction constructed by PPnCs supporting QSHE and QVHE respectively.