I see both as iconic in scifi but they take very different approaches. SW is a conflict between good and evil. This is often done really well using classic allegories of father and son, freedom vs oppression and so on. ST is about growth and exploration, self discovery and the potential of mankind.
As far as a war between the two galaxies. I see the Empire winning early on due to their overwhelming military might but as pointed out already the Federation would forge alliances with the Rebel Alliance and most likely with the other nations of the Milky way galaxy ie Klingons, Romulans,ect... This collation would eventually prove decisive as each faction shares its strengths. so you would end up with Constitution or Galaxy class star ships with cloaks launching x-wing fighters at Imperial soft targets spreading the Empires forces so thin that they could be soundly defeated in a turning point battle.