Messages on the Mac will only sync those iMessages involving the Apple ID used in Messages (Presuming you have this on your Phone as a second "Received At" ID.
iPhone to iPhone IMs will not show up in Messages on the Mac.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously
This isn't fully correct, you can add emails to your messages on both your phone and the desktop app. If people send the iMessages to any of your emeails then they can show up on both, however I am looking for a way to add my phone number to the desktop app... assuming this is not currently possible, but hoping it will be soon to fully utilize this program.