In this work, we present a comparative study of determining non-adiabatic coupling elements between localized and charge-transfer excitations in the framework GW -BSE, based on three different diabatization methods: Edmiston-Ruedenberg (ER) diabatization 17 employing explicit electronic densities and the more approximate Generalize Mulliken-Hush (GMH) and Fragment Charge Difference (FCD) formalisms. We first validate the predicted J LE-CT in a small molecule dimer system consisting of naphthalene and tetracyanoethylene (TCNE), for which reference calculations from coupled-cluster and time-dependent density-functional theory are available and allow scrutinizing the individual and combined effects of energy and (effective) wave-function predictions in the Green's functions method.