  We investigate the interplay between charge order and superconductivity near
an antiferromagnetic quantum critical point using sign-problem-free Quantum
Monte Carlo simulations. We establish that, when the electronic dispersion is
particle-hole symmetric, the system has an emergent SU(2) symmetry that implies
a degeneracy between $d$-wave superconductivity and charge order with $d$-wave
form factor. Deviations from particle-hole symmetry, however, rapidly lift this
degeneracy, despite the fact that the SU(2) symmetry is preserved at low
energies. As a result, we find a strong suppression of charge order caused by
the competing, leading superconducting instability. Across the
antiferromagnetic phase transition, we also observe a shift in the charge order
wave-vector from diagonal to axial. We discuss the implications of our results
to the universal phase diagram of antiferromagnetic quantum-critical metals and
to the elucidation of the charge order experimentally observed in the cuprates.
