Digital surface models (DSMs) extracted from very high resolution (VHR) satellite stereo images are becoming more and more important in a wide range of geoscience applications. The number of software packages available for generating DSMs has been increasing rapidly. The main goal of this work is to explore the capabilities of VHR satellite stereo pairs for DSMs generation over different land-cover objects such as agricultural plastic greenhouses, bare soil and urban areas by using two software packages: (i) OrthoEngine (PCI), based on a hierarchical subpixel mean normalized cross correlation matching method, and (ii) RPC Stereo Processor (RSP), with a modified hierarchical semi-global matching method. Two VHR satellite stereo pairs from WorldView-2 (WV2) and WorldView-3 (WV3) were used to extract the DSMs. A quality assessment on these DSMs on both vertical accuracy and completeness was carried out by considering the following factors: (i) type of sensor (i.e., WV2 or WV3), (ii) software package (i.e., PCI or RSP) and (iii) type of land-cover objects (plastic greenhouses, bare soil and urban areas). A highly accurate light detection and ranging (LiDAR) derived DSM was used as the ground truth for validation. By comparing both software packages, we concluded that regarding DSM completeness, RSP produced significantly (p<0.05) better scores than PCI for all the sensors and type of land-cover objects. The percentage improvement in completeness by using RSP instead of PCI was approximately 2%, 18% and 26% for bare soil, greenhouses and urban areas respectively. Concerning the vertical accuracy in root mean square error (RMSE), the only factor clearly significant (p<0.05) was the land cover. Overall, WV3 DSM showed slightly better (not significant) vertical accuracy values than WV2. Finally, both software packages achieved similar vertical accuracy for the different land-cover objects and tested sensors.