Dielectric barrier discharges (DBDs) are commonly used to generate cold plasmas at atmospheric pressure. Whatever their configuration (tubular or planar), the presence of a dielectric barrier is mandatory to prevent too much charge build up in the plasma and the formation of a thermal arc. In this article, the role of the barrier thickness (2.0, 2.4 and 2.8 mm) and of the kind of dielectric material (alumina, mullite, pyrex, quartz) is investigated on the filamentary behavior in the plasma and on the CO2 conversion in a tubular flowing DBD, by means of mass spectrometry measurements correlated with electrical characterization and IR imaging. Increasing the barrier thickness decreases the capacitance, while preserving the electrical charge. As a result, the voltage over the dielectric increases and a larger number of microdischarges is generated, which enhances the CO2 conversion. Furthermore, changing the dielectric material of the barrier, while keeping the same geometry and dimensions, also affects the CO2 conversion. The highest CO2 conversion and energy efficiency are obtained for quartz and alumina, thus not following the trend of the relative permittivity. From the electrical characterization, we clearly demonstrate that the most important parameters are the somewhat higher effective plasma voltage (yielding a somewhat higher electric field and electron energy in the plasma) for quartz, as well as the higher plasma current (and thus larger electron density) and the larger number of microdischarge filaments (mainly for alumina, but also for quartz). The latter could be correlated to the higher surface roughness for alumina and to the higher voltage over the dielectric for quartz.