Circuit satisfiability problem : SAT-C to SAT-2C
You can use a reduction from $\text{3-SAT}$.

$\text{3-SAT}$ is the language of $\text{CNF}$ formulas where each clause has at most three literals, and they are satisfiable, meaning - given a formula $\phi$ in the correct form, it is in $\text{3-SAT}$ iff there exists $x$ for which $\phi(x)=1$.

Now, you want to show that the language of two circuits that calculate two different functions is $\text{NPC}$, therefore, given a formula $\phi$ which is satisfiable, you want to create a reduction that transform this formula into two circuits, that calculate different functions.

First, transforming a $\text{3CNF}$ formula into a circuit can be done in polynomial time. So - you can construct one circuit. You now need to think of the other circuit. As Yuval Filmus mentioned, think of a circuit of constant size. What circuit will guarantee that if $\phi$ is satsfiable, than that circuit will calculate a different function than $\phi$, but if $\phi$ is not satisfiable, it will calculate the same function exactly?

Most of the answer is given, you are only left to think of that circuit. If you want, ask in the comments and I'll edit it in.