[en] In this Letter we quantify the trade-off between setups optimized to be ancillary to Phase II Superbeams or Neutrino Factories and experiments tuned for maximal sensitivity to the subdominant terms of the neutrino transition probability at the atmospheric scale ('maximum discovery potential'). In particular, the θ₁₃ sensitivity is computed for both Phase I superbeams (JHF-SK and NuMI off-axis) and next generation long baseline experiments (ICARUS, OPERA and MINOS). It is shown that Phase I experiments cannot reach a sensitivity able to ground (or discourage in a definitive manner) the building of Phase II projects and that this capability is almost saturated by high energy beams like CNGS, especially for high values of the ratio Δm²₂₁/vertical bar Δm²₃₁ vertical bar