  We have studied the magnetic-field-driven quantum phase transitions in
Josephson junction arrays with a large coordination number. The characteristic
energies were extracted in both the superconducting and insulating phases by
integrating the current-voltage characteristics over a voltage range 2eV\leqk_B
T. For the arrays with a relatively strong Josephson coupling, we observed
duality between the energies in the superconducting and insulating phases. The
arrays with a weaker Josephson coupling demonstrate an intermediate, "bad
metal" regime in weak magnetic fields; this observation underlines the
importance of vortex pinning at large scales and, presumably, emergent
inhomogeneity in the presence of strong offset charge disorder.
