Wind energy is usually harnessed using wind turbines but it is not the only way of collecting this energy. In this paper, Airborne Wind Energy Systems (AWES) are considered. The understanding of the wake shed by such devices is of primary importance when considering farms, yet it has not been much studied so far, and even less so when considering kites with soft curved wing. In this work, LES is used to analyse the wake of AWES. Two types of wings are considered: a straight wing, modelling the reference rigid wing AWES and a curved wing accounting for leading edge inflatable kites. Both types of wings are modelled using actuator lines. The wake analysis reveals that the wake of curved wings tends to be stronger and to recover faster. For the case of the tilted trajectory, asymmetries in the wake are also noted. The difference is explained by the azimuthal variation of the circulation distribution on the wing. It also relates to some wakes characteristics for tilted wind turbines. The wake of the curved wing is also more sensitive to the variation of the loading when it flies tilted trajectory, due to the varying loading on its tips.