The implications of elevated pressure on the statistical behavior of the flame surface density (FSD) transport statistics together with the behavior of selected established sub-models of the unclosed terms of the FSD transport equation have been analyzed in the context of large eddy simulation. For this purpose, five turbulent premixed Bunsen flames have been considered from an existing database. Four of the Bunsen flames are characterized by different pressure levels and are located on the boundary of the wrinkled and the corrugated flamelet (CF) regimes to allow for the possibility and clear identification of combustion instabilities that are often observed at high pressures. The fifth flame is in the thin reaction zones regime and serves as a reference case for the purpose of comparison. For a given filter width to flame thickness ratio, the terms of the FSD transport equation and their models behave in a qualitatively similar manner for different pressure levels. However, as the flame thickness decreases with increasing pressure, it is unlikely that a high pressure flame will be simulated for the same spatial resolution (i.e. LES filter width) normalized by flame thickness as that of an atmospheric flame. It is more likely that the spatial resolution remains constant and in this case, the modeling becomes much more challenging for higher pressures: the magnitudes of the sub-grid contributions increase for larger filter width to flame thickness ratio and thus the accuracy of sub-grid modeling is expected to play a more important role in determining the fidelity of the simulations. The flames considered in this work feature a relatively low ratio of turbulent velocity fluctuations to laminar flame speed, and under these conditions, positive values of the sub-grid curvature term and negative values of the strain rate term are observed toward the leading edge of the flame brush. This behavior cannot be captured by the well-established existing models for the sub-grid curvature term as these model expressions yield deterministically negative values. Similarly, existing models for the tangential strain term yield deterministically positive values. Detailed explanations have been provided for the observed behaviors of the unclosed terms of the FSD transport equations and their respective model predictions.