Why did the Quantum Mechanical Model replace the Bohr atomic model?
The main reason is because it offers explanatory as well as descriptive and predictive power.
The Bohr model shows that there are 2 electrons in the innermost shell, then 8, 18 and so on, but it doesn't have an explanation for why that is the case. It has descriptive power - it describes what we see - and predictive power - it correctly predicts new results.
Ideally, though, a scientific theory also has explanatory power - it explains the reason for the things is describes and predicts.
Quantum theory uses the Pauli exclusion principle to explain that each orbital can contain a maximum of two electrons, which must have opposite spins.
It shows that there is an s-orbital only in the inner shell, for 2 electrons total.
In the second shell there is an s-orbital (2 electrons) and three p-orbitals (3x2=6 electrons) for a total of 8 electrons.
In the third shell there is an s-orbital, three p-orbitals and 5 d-orbitals, each with 2 electrons, for a total of 18 electrons.
In the fourth shell we add 7 f-orbitals.
This is why the quantum theory is more powerful than Bohr's theory: it's explanatory power.