Broadband dielectric measurements at very large hydrostatic pressures (up to 1.8 GPa) are used to investigate the effect of molecular structure on the dynamical properties of supercooled di-n-butyl phthalate (DBP) and its isomer, diisobutyl phthalate (DiBP). At atmospheric pressure, both the shape of the alpha-relaxation loss peak and the fragility are essentially the same for the two materials, although the behavior of their beta-relaxations differs. The activation energy for the beta-process in DiBP, which is independent of pressure, is larger than that for DBP, while the activation volume of the former is about an order of magnitude larger. In contrast to the similarities of the alpha-relaxation at low pressure, distinct differences between the two isomers become evident at elevated pressure. The activation volume for the a-relaxation and the pressure coefficient of the glass transition temperature are significantly larger for DBP than DiBP. On the other hand, the fragility of both liquids is invariant to pressure. This latter observation corroborates recent results from high-pressure viscosity measurements on DBP, and is consistent with the invariance of the a-peak breadth to pressure. Related to the large value of the Kohlrausch stretch exponent and its invariance to pressure, there is no decoupling of the a-relaxation times and the dc-conductivity over the investigated range of temperatures and pressures. This is consistent with the idea that the decoupling of dynamic variables upon approach to T-g is a consequence of increases in intermolecular cooperativity and dynamic heterogeneity. We also compare herein the characteristic temperatures, and their associated relaxation times, at which various changes in the dynamics become manifest in the DBP and DiBP.