How hard is the Circuit Isomorphism problem? Given two circuits, how hard is it to tell if they represent the same function? Clearly, this must be at least as easy as Graph Isomorphism since you can represent any circuit as a graph.
As pointed out by @Marzio De Biasi, the problem you are asking about is $\mathsf{coNP}$-complete, by a direct reduction from TAUTOLOGY: given a boolean formula $\varphi$, is $\varphi$ equivalent to the constant 1 circuit? It is easily seen to be in $\mathsf{coNP}$. (Given that Marzio really answered the question, I suggest anyone thinking of upvoting this answer flip a coin and if it lands heads then go vote for one of Marzio's other answers.)

Let me also clarify: the problem you are asking about is more typically called Circuit Equivalence. Circuit Isomorphism is the problem: given two circuits $C_1, C_2$ on $n$ inputs, is there a permutation $\pi \in S_n$ such that $C_1(\vec{x})$ and $C_2(\pi(\vec{x}))$ are equivalent? Circuit Isomorphism has a status similar to that of Graph Isomorphism, but one level higher in $\mathsf{PH}$: it is $\mathsf{coNP}$-hard (by the same reduction above), not known to be in $\mathsf{coNP}$, in $\mathsf{\Sigma_2 P}$, but not $\mathsf{\Sigma_2 P}$-complete unless $\mathsf{PH} = \mathsf{\Sigma_3 P}$.