Please kindly consult the following report from the Swedish Meteorological Institute:
“Extended back-trajectories by means of adjoint equations“ by Lennart Robertson.
The text is available on the Research Gate.
In my personal opinion we should use both methods, although when speaking about the back trajectories we should consider the ensemble approach. The choice of the method is determined by the nature of unknown sources and the data quality.
Back trajectory methods are good for the long-range transport of pollutants; however, if the local sources are more prominent than other source analyses such as PMF, PCA is better to consider.