Performance of kd-tree vs brute-force nearest neighbor search on GPU?

I wonder if there is any study that compares the performance of kd-tree vs brute-force nearest neighbor search on GPU. Post #4 on this page suggests that kd-tree may not be the optimal algorithm for GPU but I wonder if there is any data supporting this claim?

Ultimately, naive brute-force KNN is an $O(n^2)$ algorithm, while kd-tree is $O(n \log n)$, so at least in theory, kd-tree will eventually win out for a large enough $n$. In practice, the leading constants for a GPU implementation may be vastly different --- we may be comparing $0.0001n^2$ vs $1000n\log n$ --- so it may indeed be the case that the former wins out for practical problem sizes.