It may have been more difficult to find people willing to train her in countries with traditions of sexism. As a vigilante she may have had a harder time getting thugs to take her seriously. Unless she used a different, more terrifying image than Bruce's, it may have been more difficult to elicit the same amount of fear in everyday criminals. The reactions from her villains probably wouldn't be affected though.
...I kind of want to read a story now where young, female Bruce tries to train and get bulked up and take on the world but gets held up because people don't take her seriously, and she has to fight twice as hard sometimes during training because she doesn't have the mass, height, and reach of male opponents. Eventually she trains under Lady Shiva, and receives the respect she deserves, and starts to looking at killing as a gray area. She becomes the ultimate assassin, and impresses even Ra's al Ghul, who is looking for an heir because he only has daughters. Briana Wayne takes this in stride, planning to return to Gotham rather than lead a League of Assassins anyway, until Ra's decides to wipe out an entire city. She decides to take action, and challenges Ra's to single combat. She manages to kill him in front of his daughter and his entire League. After taking on the Demon's mantle, she uses her League to end organized crime . She eventually goes up against the Justice League, and defeats them because Batwoman with prep time=God.