Occupational back-support exoskeletons are becoming a more and more common solution to mitigate work-related lower-back pain associated with lifting activities. In addition to lifting, there are many other tasks performed by workers, such as carrying, pushing, and pulling, that might benefit from the use of an exoskeleton. In this work, the impact that carrying has on lower-back loading compared to lifting and the need to select different assistive strategies based on the performed task are presented. This latter need is studied by using a control strategy that commands for constant torques. The results of the experimental campaign conducted on 9 subjects suggest that such a control strategy is beneficial for the back muscles (up to 12% reduction in overall lumbar activity), but constrains the legs (around 10% reduction in hip and knee ranges of motion). Task recognition and the design of specific controllers can be exploited by active and, partially, passive exoskeletons to enhance their versatility, i.e., the ability to adapt to different requirements.