NFA equality for automata with partial transition functions and all states accepting
The problem is PSPACE-complete, by reduction from the equivalence problem for NFAs.

Suppose we are given two NFAs $A_1,A_2$ over an alphabet $\Sigma$. Let $\dashv$ be a new symbol. To each of the NFAs we add two new states $q_f,q_t$, and the following transitions:


An $\epsilon$-transition from the initial state to $q_t$.
A self-loop on $q_t$ labeled $\Sigma$.
A transition labeled $\dashv$ from every accepting state to $q_f$.


Let $B_1,B_2$ be the new NFAs, after making all of their states accepting. Then
$$
L(B_i) = \Sigma^* \cup (L(A_i)\dashv).
$$
Therefore $L(A_1) = L(A_2)$ iff $L(B_1) = L(B_2)$.