Single crystal EPR studies on (NH,),CU(SO,)~ ' 6 H,O and K,CU(SO,)~ . 6 H,O in the temperature range 4.2 to 360 K show that the vibronic g-factor averaging is completed in the ammonium salt at 340 K but not in the potassium salt. The vibronic effects are discussed in terms of a thermally activated two-level model which shows that the barrier between two wells of the adiabatic potential surface increases at low temperatures and tends to zero at high temperatures. Exchange coupling effects are different in the ammonium and the potassium salts. The coupling between inequivalent Cu sites appears below 100 K in the ammonium salt and grows up to J = 0.0023 cm-at 4.2 K. This coupling is not observed in potassium salt where, moreover, the coupling between equivalent sites is very small allowing the hyperfine structure to be more resolved at low temperature. A giant line broadening and line shift are observed below 30 K in the potassium salt. The above effects are discussed in relation to the possible superexchange pathways and differences in the space distribution in the electron density of the ground state of Cu(I1) in both crystals.