  We study Schr\"odinger operators on compact finite metric graphs subject to
$\delta'$-coupling conditions. Based on a novel modified local Weyl law, we
derive an explicit expression for the limiting mean eigenvalue distance of two
different self-adjoint realisations on a given graph. Furthermore, using this
spectral comparison result, we also study the limiting mean eigenvalue distance
comparing $\delta'$-coupling conditions to so-called anti-Kirchhoff conditions,
showing divergence and thereby confirming a numerical observation in
[arXiv:2212.12531].
  .
