Thermal expansion, electrical resistivity, magnetization, and specific heat measurements were performed on URu_2-xFe_xSi₂ single crystals for various values of Fe concentration x in both the hidden-order (HO) and large-moment antiferromagnetic (LMAFM) regions of the phase diagram. Our results show that the paramagnetic (PM) to HO and LMAFM phase transitions are manifested differently in the thermal expansion coefficient. The uniaxial pressure derivatives of the HO/LMAFM transition temperature T₀ change dramatically when crossing from the HO to the LMAFM phase. The energy gap also changes consistently when crossing the phase boundary. In addition, for Fe concentrations at x_c ≈ 0.1, we observe two features in the thermal expansion upon cooling, one that appears to be associated with the transition from the PM to the HO phase and another one at lower temperature that may be due to the transition from the HO to the LMAFM phase.