Closure properties of finite state transducers
It is probably a better idea first to concentrate on the complement, i.e., the equality language $\{ w\in \Sigma^* \mid T_1(w) = T_2(w) \}$.

Also, simple FST's will do, as even for morphisms $h_i: \{a,b\} \to \{1\}^*$, $\{ x\in \{a,b\}^* \mid h_1(x) = h_2(x) \}$ need not be regular.

And I want to add that it has been shown that $\Delta(T_1,T_2)$ is always context-free.