I think the simplest way to answer that is that there are probably almost as many ideas on what transgenderism/ transvestism means as there are people who identify that way. Some dress up only in secret; others are more open. Some try to look as feminine as possible; for others it's enough to wear the clothes. Some attempt to "blend in" to the crowd; others are rather less bothered about not being noticed. And all sorts in between.
Conchita Wurst seems to be taking up a sort of "half-way house" approach, it seems. Take away the beard and she'd look fairly convincing. But that's not what she's wanting to do, apparently. Instead, she's gone for a visual fusion between the two sides of his/ her life. Meant to be thought-provoking. Whether it is or not is rather up to you, but in the end, like almost everyone else, she is just trying to be herself.