I think the greater tech levels of the ST universe would give an edge to the Federation's forces.
If my memory of the SW movies is accurate, the shielding tech of the SW universe (and thus, the Empire) is far behind that of the Federation.
SW shields seemed simply designed to deflect incoming fire, but could be overwhelmed by repeated strikes.
On the other hand, ST shields seem to be multi-purpose and very adaptable, so tuning them to simply be unaffected by laser fire seems very possible.
I note that ST energy weapons were adjustable, while SW energy weapons were much less so, at least judging from the movies.