Suspensions of poroelastic particles are indispensable for applications where tailoring the overall properties is a necessity. The single-particle elastic network gives rise to their elastic behavior, while the flow of the viscous solvent through the particle structure gives rise to their rate-dependent behavior. In this work, we study the effect of the single-particle elastic modulus and permeability on the properties of the entire poroelastic-particle suspension subject to simple-shear deformation. For this purpose, the dynamic two-scale model developed by Hütter et al. [Faraday Discuss. 158, 407-424 (2012)] is used. Upon deformation, both permeable- and impermeable-particle suspensions undergo a transition from a glassy state to a shear-induced ordered state. On the one hand, the particle permeability is found to affect the rate at which the ordered state is reached. At a fixed elastic modulus, increasing the particle permeability prolongs the time scale at which shear-induced ordering occurs. On the other hand, the long-time shear stress values are dominated by the elastic properties of the individual particle, through a sublinear dependence. This is due to the fact that, the lower the particle elastic modulus, the larger are the occurring particle-volume changes, which in turn has ramifications for the dynamics and the mechanical behavior of the suspension.