It's easy to prove Borel-Wadge determinacy from Borel determinacy. But it's often said that Borel-Wadge determinacy is 'much weaker' than the latter. This is then argued by showing models in which the former is true but the latter false.
But is there also a proof of Borel-Wadge determinacy that doesn't use Borel determinacy, and in that way shows it's 'much weaker'?