Bohr's model assumes quantized orbits in which the electrons can move without the emission of radiant energy. The quantum mechanical model has a similar feature of quantized orbits even though it is more rigorous.
The Bohr's atomic model although assumes that the energy of the electron depends only on the principle quantum number (n) of the orbit.
The quantum mechanical model uses four basic quantum numbers to specify an electron.
Though the very basic idea of quantized (discrete) states/ energy levels is the same in the Bohr's model and the Quantum mechanical model, the latter provides with a much more satisfying theory than the former by introducing more quantum numbers to accurately specify the electron's energy.
Differences between the two exist, the most important being that the path of the electron is well defined in the Bohr's model while the Quantum mechanical model totally discards the idea of finding the electron trajectory and relies solely in the probability of finding an electron in a given region of space.