The future of air traffic management moving to 4D trajectory-based operations will require the development of new airspace sectors to increase aircraft capacity and advanced 'human-centered' decision support tools for future air traffic controllers. To evaluate and aid in the design of future air traffic management systems, complexity metrics would help to speed up the development of advanced safe air traffic management systems. Although an airspace sector may look 'complex' with many aircraft, this does not equate to it actually being complex with the right tool. The complexity of a sector or traffic scenarios depends on a large number of factors, irrelevant of the tool. Previous studies with well developed state-based complexity metrics focused on air traffic controllers safely controlling traffic of today, with a 'hands-on' approach. One recent metric based on trajectory-based management could prove to help predict controller workload. The goal of this study has been to empirically investigate if a complexity metric can predict human controller workload in future 4D trajectory management environments. For this purpose a previously developed 4D management tool had been used to support a controller in an envisioned future large airspace sector with varying traffic structures and perturbation levels. A well developed state-based complexity metric was compared against a recent trajectory-based complexity metric by the results of the reported workload experienced. Results of a human-in-the-loop experiment indicate that the trajectory-based complexity metric looks promising to workload predictions in 4D trajectory management environments.