Airborne Wind Energy (AWE) is an emerging technology in the field of renewable energy that uses kites to harvest wind energy. However, unlike for conventional wind turbines, the wind environment in AWE systems has not yet been studied in much detail. We propose a simulation framework using Large Eddy Simulation to model the wakes of such kite systems and offer a comparison with turbine-like wakes. In order to model the kite effects on the flow, a lifting line technique is used. We investigate different wake configurations related to the operation modes of wind turbines and airborne systems in drag mode. In the turbine mode, the aerodynamic torque of the blades is directly added to the flow. In the kite drag mode, the aerodynamic torque of the wings is directly balanced by an opposite torque induced by on-board generators; this results in a total torque on the flow that is zero. We present the main differences in wake characteristics, especially flow induction and vorticity fields, for the depicted operation modes both with laminar and turbulent inflows.