The Bohr theory permits us to visualize the structure of the atom, whereas quantum mechanics is very complex and concerned with such ideas as wave functions and probabilities. What reasons would lead to the replacement of the Bohr theory by quantum mechanics?
The Bohr model is a highly accurate theory for atomic structure and it even appears as the solution to a select number of Quantum Mechanics problems. When one picks the Quantum Mechanics version of structure over the Bohr one they are truly being a nitpick (or doing some real experiments). There are a few discrepancies that only someone running the numbers would ever notice.
For example, the biggest error (that Wikipedia states) is the prediction of Bohr that the ground-state electrons would have an orbital angular momentum of ћ (pronounced "h-bar") when they were observed to have 0. As you can see the terms involved are complex and one would only notice by measuring.
There are several other errors that I had to research before I could tell you with a certainty just why the Bohr model is not a correct theory. As you can probably guess these errors are even more esoteric than the "biggest" one as stated by the Wiki. All of them have to do with spectral emission lines of atoms.
Things like the Zeeman effect whereby if you influence the atom with a magnetic field and you excite an electron up an orbital only to observe its photon-emission (when it comes back down) that this line is influenced by the magnetic field. The Bohr model does not have any terms for 'external magnetic field' within the Balmer formula (the equation that determines the energy of the spectral lines).
As you can see, there are few reasons why the Bohr model is not used in labs and even then most physicists doing calculations only use the true Quantum model if they expect the Bohr model to not truly represent their apparatuses. The Bohr model is an exceedingly good one that was made with almost no lab measurements beforehand.
There is one good reason for preferring the ideas of quantum theory to that of Bohr's model and that is that engineers use the equations of quantum electrodynamics on an everyday basis when they are, for example, designing nuclear power stations, and in practice, the equations work very exactly.
It is not a question of replacing one theory with another. Here we have a picture of the evolution of knowledge which is what science is all about.
From five elements to metals and non metals to indivisible atoms to protons neutrons and electrons and to quantum theory. That is not the end. We still haven't all the answers. We go on searching for more clarity on quantum mechanics as well as cosmic puzzles. The more we learn the more complex the picture is going to be. We cannot put a full stop to our quest for knowing more and exploring the frontiers of knowledge. It is in human nature to go on seeking the frontiers of knowledge.