The ground state of U Ru2 Si2 changes from so-called hidden order (HO) to large-moment antiferromagnetism (LMAF) upon applying hydrostatic pressure in excess of ∼14 kbar. We report the dc magnetization M (B,T,p) of U Ru2 Si2 for magnetic fields B up to 12 T, temperatures T in the range 2-100 K, and pressure p up to 17 kbar. Remarkably, characteristic scales such as the coherence temperature T*, the transition temperature T0, and the anisotropy in the magnetization depend only weakly on the applied pressure. However, the discontinuity in MT at T0, which measures the magnetocaloric effect, decreases nearly 50% upon applying 17 kbar for M and B parallel to the tetragonal c axis, while it increases 15-fold for the a axis. Our findings suggest that the HO and LMAF phases have an astonishing degree of similarity in their physical properties, but a key difference is the magnetocaloric effect near T0 in the basal plane.