We used classical molecular dynamics simulations to investigate the morphology and proton transport properties of perfluoro phosphonic (FPA) and phosphinic acid (FPA-I) membranes that have potential applications in low-temperature fuel cells. We systematically investigated these properties as a function of the hydration level. We examined changes in structure, transport dynamics of water and hydronium ions, and water network percolation relative to those in Nafion membrane to examine the effect of functional group acidity on these properties. Phosphonic and phosphinic acid moieties in FPA and FPA-I have lower acidity than sulfonic acid in Nafion, yet the diffusion of water was faster in FPA and FPA-I than in Nafion, particularly at low hydration levels. However this did not give rise to notable differences in hydronium ion diffusion and water network percolation for these membranes over Nafion. These results, along with similar findings from our recent study of perfluoro-sulfonyl imide membranes carrying stronger superacids than the sulfonic acid of Nafion, suggest that there is no strong correlation between the acidity of the functional groups and the dynamics of water and hydronium ions in hydrated polymer electrolyte membranes with similar fluorocarbon backbones and side chains.