  Asymptotic dimension and Assouad-Nagata dimension are measures of the
large-scale shape of a class of graphs. Bonamy et al. [J. Eur. Math. Society]
showed that any proper minor-closed class has asymptotic dimension 2, dropping
to 1 only if the treewidth is bounded. We improve this result by showing it
also holds for the stricter Assouad-Nagata dimension. We also characterise when
subdivision-closed classes of graphs have bounded Assouad-Nagata dimension.
