The Incremental Sheet Forming (ISF) process offers a large variety in tool path strategies to obtain a particular final product shape. As fundamental understanding of the relevant deformation modes in ISF is growing, the selection of the tool path strategy may be shifted from trial-and-error towards more fundamentally based knowledge of the process characteristics. Truncated cones and pyramids have been fabricated by both unidirectional (UD) and bidirectional (BD) contour-based tool path strategies, considering different wall angles and materials (Mn-Fe alloyed aluminum sheet and low carbon steel sheet). It is shown that the induced through-thickness shear along the tool movement direction is clearly non-zero for UD, in which case the sense of tool movement is the same for all contours, while it is close to 0 for BD, due to the alternating tool sense during consecutive contours. Furthermore, the heterogeneity in product thickness, as observed for the UD strategy in [1,2], is avoided by using the BD strategy. It is verified that this difference in deformation may affect the mechanical properties in the walls of pyramids by means of tensile testing, but the results are material-dependent. For the aluminum alloy, the re-yield stress along the tool movement direction is smaller for BD in comparison to UD, and the fracture strain in large wall angle products is higher. For the steel, no statistically significant differences in mechanical properties between UD- and BD-processed parts are observed. Finally, for both materials a (slightly) higher limiting wall angle has been repeatedly measured using the BD tool strategy. In light of these results, the bidirectional tool path strategy is to be preferred over the unidirectional one, as thickness distribution and formability are more favorable, while both strategies require similar resources and processing time.