This paper proposes two novel convolutional neural networks for 3D object classification, tailored to process point clouds that are composed of planar slices (profiles). In particular, the application that we are targeting is the classification of vehicles by scanning them along planes perpendicular to the driving direction, within the context of Electronic Toll Collection. Depending on sensors configurations, the distance between slices can be measured or not, thus resulting in two types of point clouds, namely metric and non-metric. In the latter case, two coordinates are indeed metric but the third one is merely a temporal index. Our networks, named SliceNets, extract metric information from the spatial coordinates and neighborhood information from the third one (either metric or temporal), thus being able to handle both types of point clouds. Experiments on two datasets collected in the field show the effectiveness of our networks in comparison with state-of-the-art ones.