Are Boolean circuits 'universal'
It is important to remark that a specific boolean circuit only treats inputs of a given size, unlike a Turing Machine that can take inputs of any size.

So a language with inputs of arbitrary size is usually treated by a family of circuits, one for each size of input.
The problem with this definition is that it allows circuit to solve uncomputable problems, since we could for instance answer 1 if $|x|\in H$ and $0$ if $|x|\notin H$, where $H\subseteq \mathbb N$ is any set. Take for instance $H$ to be an enconding of the halting problem.

To circumvent this problem, we usually look at uniform families of circuits, where there is a fixed Turing Machine $M$ which on input $n$ outputs the circuit for size $n$ inputs.

There is now a hope that circuits are equivalent to Turing machines.

Unfortunately, the model of circuits have computations that always halt (or you can define circuits with loops that never halt but they are useless). This limitation alone suffices to prove that they cannot be Turing complete, because any Turing-complete model must allow infinite computation.

However notice that you have a uniform family of circuits for any language that is decided by a total Turing machine: on input $n$ you can build your circuit for size $n$ by listing all inputs of size $n$ accepted by your machine.
The things that you miss are recursively enumerable languages, such as the Halting problem.