Phase diagrams of polyvinylidene fluoride (PVDF) and its copolymers with hexafluoropropylene (HFP) and bromotrifluoroethylene (BTFE) are investigated via first-principles simulations and compared to previously studied P(VDF-chlorotrifluoroethylene) (CTFE) data. We find that a nonpolar to polar phase transition induced by an electric field also occurs in HFP and BTFE copolymers and the results for P(VDF-HFP) show good agreement with existing experiments. For P(VDF-BTFE) we show that its nonpolar phase remains the ground state for a substantially larger range of concentrations than for P(VDF-CTFE) and P(VDF-HFP), and predict that a high BTFE concentration copolymer will achieve a significantly higher energy density at low field than P(VDF-CTFE) 9%. The transition pathways connecting the polar and nonpolar phases are also calculated and the energy barriers for the transitions turn out to be similar for the three copolymers, even at different co-monomer concentrations. The similarity of barriers indicates that a mixture of these and related copolymers can be used to optimize the properties of the dielectric, such as energy density, processability, and cost.