Semi-automated parts-to-picker systems are becoming more popular in order picking, making efficient rack designs for fast searching and picking more important. Virtual reality (VR) using modern head-mounted devices (HMD) is a promising technology for the human-centred planning of order picking at single racks. However, state-of-the-art HMDs come with several limitations. For evaluating the usability of HMDs, it is of interest whether these limitations lead to different workload and measured times in VR compared to a real environment. An experimental setup consisting of a real rack and an equally sized virtual representation (using the HTC Vive HMD) has been developed for a randomized controlled study with 112 participants and 10 professional order pickers. This dataset contains the raw data obtained during the experimental study. Contains total order completion times, registered picking errors, orders with dropped items, questionnaire results (including NASA-TLX), and timestamp data from infrared sensors recognizing each interaction of the participants with the picking racks.