Catalytic exhaust after-treatment for the reduction of carbon monoxide and hydrocarbons, using flow-through monolithic reactors, is a well-proven technology in commercial diesel engines. However, recently, most diesel exhaust systems have started to be additionally equipped with wall-flow particulate filters. Most commercial filters are also catalyst-coated, which gives the potential option to combine oxidation and filtration functionalities in a single reactor. The present study compares the steady-state and transient performance characteristics of catalyzed wall-flow diesel particulate filters to the respective flow-through oxidation catalysts. The comparison is based on a theoretical basis, using mathematical models previously published and experimentally validated. It is shown that the conversion efficiency of the wall-flow catalyzed filter is a complex function of thermal, mass-transport, and chemical phenomena that occur simultaneously. Under steady-state conditions, the wall-flow reactor has a higher conversion efficiency, compared to a respective flow-through with the same dimensions and catalytic loading, under mass-transfer-limited conditions ( high temperature, high flow rate). Under kinetically limited conditions, both systems perform identically. The transient performance during a simulated cold-start operation of the wall-flow reactor is shown to be inferior, compared to the flow-through one. The phenomena are analyzed and explained in detail by examining the time-dependent profiles of flow distribution, temperature, and species concentration in both reactors.