Ordered crystalline microporous materials such as zeolites, metal-organic frameworks (MOFs), and zeolitic imidazolate frameworks (ZIFs) offer considerable potential for separating a wide variety of mixtures. There are basically two different separation technologies that can be employed: (1) pressure swing adsorption (PSA) unit with a fixed bed of adsorbent particles, and (2) membrane device, wherein the mixture is allowed to permeate through thin micro-porous crystalline layers. The fundamental physico-chemical principles underlying the separations in these two devices are fundamentally different. In fixed bed adsorbers, diffusional effects are usually undesirable because these tend to produce distended breakthroughs and diminished productivities. For membrane separations, both intra-crystalline diffusion and mixture adsorption equilibrium determine permeation selectivities, and diffusion selectivities are often the primary drivers for separations. Using Configurational-Bias Monte Carlo (CBMC) simulations of mixture adsorption equilibrium, and Molecular Dynamics (MD) simulations of guest diffusivities in a wide number of guest/host combinations, we demonstrate that adsorption and diffusion do not, in general, proceed hand-in-hand. Strong adsorption often implies lowered mobility. Consequently, the best material for use in fixed bed adsorbers does not always coincide with the ideal choice for use as thin layers in membrane devices. Methodologies for screening micro porous materials for use in fixed-bed units and membrane devices are discussed using a large number of examples of industrially important separations.