Hi,
The app is called Messages.
iMessages is what the iMessage account can do to other Apple ID and iPhone numbers.
The GoogleTalk or jabber account is nothing to do with iMessages.
In iChat 4 and 5 (I can not check 3 at the moment where Jabber was added) the iChat app had the same Priority as the Web Login to Google had.
This means the Server at Google could not decide which login should get the IMs.
It would tend to default to the Last login.
The Messages app lets you set the priority for the App
Lower numbers are "better" in that they get the messages first.
You can then set up different priorities for your home computer, work computer and phone so that one will override the other so that you are never out of contact.
I would check the priorities used in Pidgin, Adium and Messages on both computers.
10:43 PM Friday; November 23, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously