In the Stan user's manual (Version 2.0.1, page 157), it says
A hierarchical model such as the above will suffer from the same kind of inefficiencies... [for a Hamiltonian Monte Carlo method] because the values of
sigma_betaare highly correlated in the posterior
They then recommend reparameterizing the model to avoid this issue.
I'm not sure I have good intuition about why correlations would be a problem. I thought that the whole point of Hamiltonian Monte Carlo was that it was invariant to rotation. So it shouldn't matter whether the posterior is aligned with the axes or if correlations put the major axis at an angle.
The best guess I can come up with is that, if the correlations get to be extreme enough, the posterior could end up very long and narrow, and that something about the difference in scales causes problems. But I'm not sure that this is a reasonable interpretation.