First, I've successfully downgraded from Mavericks to Mountain Lion on my Macbook Pro with Retina display. I hope you have good TimeMachine Backups.
The sync capability is not (necessarily) a function of the version of iTunes but it is part of the operating system. Apple has removed the local sync (WiFi or USB) capablities for Contacts and Calendar from Mavericks, Mac OS X 10.9. Contacts and Calendar, along with Notes (moved in a previous OS 'upgrade') are now ONLY synced via iCloud. FYI, the KeyChain is also apparently exported around the Internet via iCloud; good move.
As I did not want my confidential information out of my direct management, after a week of running Mavericks, I decided to go back to Mountain Lion. I hope Apple will recitfy this.
As an FYI, I did NOT start using iCloud. Before I upgraded, I did NOT know that iCloud was required. Since I never have used iCloud, I skipped that part of the Mavericks install or startup.
To down grade to Mountain Lion (10.8.5), I rebooted the Mac into Recovery Mode and restored my computer from a TimeMachine backup from just before I did the upgrade. After this, I had my computer back to the state just before the upgrade.
Next, I wanted to recover all my user files and work I had done since the upgrade. After I started the Mac, I logged into another account (my admin account). From there, I restored the latest /Users hierarchy to bring my email, and other info (calendar, contacts list, etc.) from TimeMachine. After this, I had the old operating system and my current user files.
But wait, there's more; we are not finished yet. The iPhoto program in Mavericks makes some changes that are not backward compatible. SO, I restarted the Mac (just to be safe) and logged back into my regular account. I then restored the contents of ~/Pictures from the TimeMachine from just before the Mavericks upgrade.
All seems to work quite well (Calendar, Contacts, iPhoto, iTunes syncing, Mail, etc.).
I hope this helps.