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In this work, we have solved the Bohr Hamiltonian with a deformation-dependent mass term in the presence of the free parameter χ by using the Nikiforov-Uvarov (NU) method. We have studied such Hamiltonian by employing the generalized Kratzer potential for the β part of the total potential. While in γ -angular parts, we have used both axially symmetric prolate deformed nuclei and γ -unstable nuclei. The energy eigenvalues and the corresponding wave functions have been calculated to investigate the competition between γ -stable and γ -rigid ( γ -unstable and γ -rigid) collective conditions. Also, the energy spectra and transition rates have been determined for some nuclei and compared with experimental data. Our results show good agreement with experimental data.