Setting tune to 0 disables the step size adaptation from the paper. Without step size adaptation we just use the initial guess (which only depends on the dimension). Bad step sizes can lead to arbitrarily inefficient sampling and there is no reason to assume that the initial guess in in any way reasonable.
It has also been known long before nuts was written, that the mass matrix is important for hamiltonian methods. I don’t see what a comparison would tell you if you disable one of the features that makes nuts useful in the first place.
We do not implement the exact algorithm from the paper anymore, there have been some changes since. We take into account the energy change when sampling from the tree for example.
Edit: I forgot to pass in step=step into pm.sample in the last post.