Atmospheric pressure dielectric barrier discharges (DBDs) can remove harmful components from gas streams energy efficiently and with short switch-on and -off times based on excess renewable energies. Two classical types of DBDs are frequently used, packed bed volume and surface DBDs, where gas conversion is induced by volume or surface streamers, respectively. Such discharges are often unstable and diagnostics are difficult to apply to them. In this work, a novel type of patterned DBD (pDBD) is used, that includes custom shaped dielectric pellets immersed into one of the electrodes at strategically selected positions, and its performance for volatile organic compound (VOC) conversion at the example of n-butane in helium carrier gas is studied experimentally as a function of control parameters such as driving voltage, frequency, reactor design, gas flow, and composition. For rectangular driving voltage waveforms 10 kHz, the presence of structured electrodes leads to an electric field distribution that generates controlled streamer propagation paths, and induces the simultaneous presence of both volume and surface streamers. Due to this synergistic combination of volume and surface DBDs, the energy efficiency of n-butane conversion is found to be enhanced significantly compared to classical DBDs, reaching approximately 0.5×10^17 1/J. This is explained by correlations of measured conversion, power dissipation in the plasma, and spatio-temporally resolved streamer dynamics as a function of external control parameters. Admixing oxygen is found to drastically enhance n-butane conversion and energy efficiency, reaching approximately 85% and 2.5×10^17 1/J, respectively, in pDBDs via oxidation caused by reactive oxygen species generated in the plasma.