pound We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and deformable particle (DP) model that we developed for bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at fixed area to avoid overlap during compression. We compare the structural and mechanical properties of jammed packings generated using the SP and DP models as a function of the packing fraction rho, instead of the reduced number density phi. We show that near jamming onset the excess contact number Delta z = z - z(J) and shear modulus G scale as Delta rho(0.5) in the large system limit for both models, where Delta rho = rho - rho(J) and z(J) approximate to 4 and rho(J) approximate to 0.842 are the values at jamming onset. Delta z and G for the SP and DP models begin to differ for rho greater than or similar to 0.88. In this regime, Delta z similar to G can be described by a sum of two power-laws in Delta rho, i.e. Delta z similar to G similar to C-0 Delta rho(0.5) + C-1 Delta rho(1.0) to lowest order. We show that the ratio C-1/C-0 is much larger for the DP model compared to that for the SP model. We also characterize the void space in jammed packings as a function of rho. We find that the DP model can describe the formation of Plateau borders as rho -> 1. We further show that the results for z and the shape factor A versus rho for the DP model agree with recent experimental studies of foams and emulsions.