Context. B-type asteroids constitute a peculiar spectral class within the C-complex. Previous work has pointed out the difference between the visible geometric albedos of B-types and those of the Pallas collisional family (PCF), whose few members with observed spectra are B-types (one exception out of eight objects). This has been interpreted as being due to compositional differences. However, the PCF members are typically smaller than the spectroscopically classified B-types, and the following possibilities have not been ruled out: the albedo differences might be related to a size-albedo dependence and/or to the generally larger errors of the WISE data and best-fitting values of the derived parameters expected for smaller objects. Aims: We compare albedos and beaming parameters of PCF members and B-types of similar sizes and re-examine our conclusion on the different composition of the PCF. Methods: By modelling their WISE/NEOWISE data, we derived sizes and albedos of all objects whose Sloan Digital Sky Survey reflectances are similar to the typical B-type reflectance spectra. In particular, we derived the so-called infrared beaming parameters (η), effective diameters (D), and corresponding visible geometric albedos (pV), and studied their value distributions. Results: We obtained the effective diameter and geometric visible albedo for ~600 B-type asteroids whose sizes range between 2 and 100 km, approximately half of which have fitted η-values that are inversely correlated to size. We found that the albedo distributions of the PCF is significantly different from that of other B-types in the same size range (2-20 km), and we rule out any size-albedo dependency or biases related to the lower quality of the pV-values of smaller objects. In addition, we also found differences between the η-value distribution of the PCF and the other similarly-sized B-types. Conclusions: The differences in the visible albedos of PCF members and the other B-types of similar sizes is a strong indication that their compositions are different. The trend between beaming parameter and size of the B-types (excluding the PCF) is consistent with the expectation that the surfaces of smaller asteroids have coarser rocks than do those of larger objects (D> 40 km), which are thought to be covered by a finer, more insulating layer of dust. Full Table 1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/591/A14