IOS – Jabber XMPP chat client for iOS with push notifications

So the answer to my question is to use Adium. A lucky discovery: I was about to disconnect my chat account using the File menu, but when I moused over the text "Disconnect: ...", a context menu appeared as one might expect. However, I had never clicked the item labeled Discovery Browser. Under the server's "Public Chatrooms" I found a list with the JID of all the active chat rooms.

Just of note that Facebook is notorious for being extremely flakey when delivering notifications of any kind (whether they be system wide through the home screen icon, or even in-app). If you have Push enabled on both devices, the problems could lie within Facebook.

Also note that it may (read: should) be the case that when you check your account on one device, the notifications should disappear on the other, as they will be marked as read.

Additionally, it could be that Facebook's servers deliver a notification only once to any waiting device capable of handling them (remember they have millions of users to contend with). You'll have to contact Facebook to make certain of this however.

You can use mail to test it. If you send yourself an email, do you receive notifications on both devices? If you read the mail, do they disappear (get marked as read) on both devices?