Consider two chain complexes $A_\bullet$ and $B_\bullet$ in your favorite category $\mathcal{C}$ (say abelian groups, or vector spaces). The question is:
Q1: Are there standard techniques to show that $A_\bullet$ and $B_\bullet$ are not isomorphic?
To avoid trivial cases, we may assume that $A_\bullet$ and $B_\bullet$ are homotopic (or at least have the same homology, assuming homology makes sense in $\mathcal{C}$) and that $A_\bullet$ and $B_\bullet$ have isomorphic chain spaces.
Note: the question is motivated by the similar question on non-homotopic complexes, where an answer could be "compute the respective homologies (assuming it makes sense) and hope they are distinct: in many practical cases, this is enough".
Added: to give a more precise question:
Q2: Are there examples of homotopic complexes with isomorphic chain spaces, but which are not isomorphic?