We present the first pilot study of jets from young stars conducted with X-shooter, on the ESO/Very Large Telescope. As it offers simultaneous, high-quality spectra in the range 300-2500 nm, X-shooter is uniquely important for spectral diagnostics in jet studies. We chose to probe the accretion/ejection mechanisms at low stellar masses examining two targets with well-resolved continuous jets lying on the plane of the sky: ESO-HA 574 in Chameleon I and Par-Lup3-4 in Lupus III. The mass of the latter is close to the sub-stellar boundary (M sstarf = 0.13 M ☉). A large number of emission lines probing regions of different excitation are identified, position-velocity diagrams are presented, and mass outflow/accretion rates are estimated. Comparison between the two objects is striking. ESO-HA 574 is a weakly accreting star for which we estimate a mass accretion rate of $\log (\dot{M}_{{\rm acc}}) = -10.8 \pm 0.5$ (in M ☉ yr–1), yet it drives a powerful jet with $\dot{M}_{{\rm out}}$ ~ 1.5-2.7 × 10–9 M ☉ yr–1. These values can be reconciled with a magneto-centrifugal jet acceleration mechanism assuming that the presence of the edge-on disk severely depresses the luminosity of the accretion tracers. In comparison, Par-Lup3-4, with stronger mass accretion ($\log (\dot{M}_{{\rm acc}}) = -9.1 \pm 0.4$ M ☉ yr–1), drives a low-excitation jet with about $\dot{M}_{{\rm out}}$ ~ 3.2 × 10–10 M ☉ yr–1 in both lobes. Despite the low stellar mass, $\dot{M}_{{\rm out}}$/$\dot{M}_{{\rm acc}}$ for Par-Lup3-4 is at the upper limit of the range usually measured for young objects, but still compatible with a steady magneto-centrifugal wind scenario if all uncertainties are considered.