It would be nice to be able to run this from the command-line.
If the automata are minimal WDBA, this is easier, since they can be complemented in linear time. Löding (/Efficient minimization of deterministic weak ω-automata/, 2001) discusses such equivalence check in its last paragraph. Dealing with DBA that are not weak is also easy.
In the general case we would have to use some complementation algorithm (but I'd prefer that we reimplement Safra's construction — see #16 (closed)). Maybe we can also avoid the cost of Safra in case the automata are isomorphic.