My WebRTC app works fine when I connect two of the same browsers, but when I try a combination neither respond to each others signaling messages. Something probably worth mentioning is that I have not implemented TURN, however I don't see why that should make a difference so I'm not going to change that unless I'm fairly certain it will.
I don't have much of a clue where the error lies, so I will just add code on request for the sake of readability.
Make sure you enable DTLS-SRTP (Firefox only supports DTLS-SRTP) by passing the following to the PeerConnection constructor:
{ 'optional': [{'DtlsSrtpKeyAgreement': 'true'}]}
See this page for more details.