From Longman Dictionary of Contemporary Englishwin out phrasal verbSUCCEED IN DOING somethingto finally succeed or defeat other people or things over Often presentation wins out over content (=is treated as more important than content). → win→ See Verb table
Examples from the Corpus
win over• Style wins out over substance all the time, everywhere.• Style wins out over substance too often in Hollywood movies.• Ultimately, the cornfields of Lawrence won out over the palm trees of Westwood.• It remains to be seen whether the archaeologists will win out over the urban planners. 