As well as all the hocus-pocus we get about wands, there's also the lone voice of Hermione saying it's the wizard not the wand that's important. Harry's problems with the blackthorn wand are about confidence - he's lost in the woods and he's lost his original wand with it's link to Voldemort's that he's come to think of as a safety net.

I think the elder wand is simple: it belongs to the most powerful wizard, and the most powerful wizard is the one who wins it, whether that's by duelling or by nicking it from a dead body. For me, all that stuff Harry says to Voldemort in their stand-off at Hogwarts is bluff, really. Harry is just undermining Voldemort's confidence. Harry wins the wand because Voldemort is afraid of him, while Harry is not afraid of Voldemort - for the very good reason that Voldemort's spells no longer work!