What do the Bohr and quantum mechanical models have in common?

In both models, electrons move around a positively charged nucleus filling different energy levels called shells.

Explanation:

Bohr's model places electrons in ascending energy levels orbiting in a circular motion around the nucleus. The quantum mechanical model also places electrons around a positively charged nucleus following ascending energy levels, but this time these don't move in a circular manner but instead randomly inside clouds of probability.

In the Bohr Model, the electron is treated as a particle in fixed orbits around the nucleus. In the Quantum Mechanical Model, the electron is treated mathematically as a wave.