Automation in a domestic environment is not flawless and human interference will be necessary, for implementing robots in this environment. When remotely controlling semi-autonomous robots, proposed concepts can be divided into two main concepts: To trade control back and forth between the human and the operator and to share control continuously. However, a deep analysis lacks about when either of these methods is useful. This study focuses on comparing task completion time and task behavior Trading Control (TC) and Haptic Shared Control (HSC) using a mix of accurate models of the tasks and models with a small translational offset. These are examined in the current mix as well as separated into models that were accurate or did contain an offset. In remote execution of a constraint motion task, we hypothesize Haptic Shared control to have a lower task completion time compared to Trading Control when inaccuracies are present. When the model is fully accurate, on the other hand, we hypothesize Trading Control to have a lower task completion time compared to haptic shared control. Participants used a 6DOF haptic manipulator to control a virtual robot arm, in order to open a simulated drawer. An autonomous controller was developed based on a model that was perfectly accurate (50% of the time), or that had an effective endpoint error (50% of the time). Control over the automation was either traded by pressing a space bar or continuously shared through haptic shared control. In trials with a translational offset, Haptic shared control had a lower task completion time compared to trading control. In the trials with a perfectly accurate model of the task, Trading Control had the benefit of lowering peak collision force and increasing smoothness of the master input. Therefore more research is needed to better understand when trading control is beneficial compared to haptic shared control.