I had a very similar problem - iPad 3, upgraded to iOS 6, but no Siri. When I say "no Siri" I mean no option to set up or enable Siri under Settings - > General or otherwise. Siri was not installed with iOS 6, even though the upgrade appeared to complete without incident. I have seen postings by a few other users who have had the same problem.
I went through a complete set of troubleshooting steps with an Apple tech on the phone, including doing a complete reset of all iPad settings. Still, no Siri. In the end, I had to completely restore my iPad to the factory defaults to get Siri on the device by connecting the iPad to my computer and selecting "Restore" under the Version heading. When the factory wipe and restore completed, I had to set my iPad up from scratch under a completely new profile, not from my old backup.
The Apple tech's only explanation was that it must have been a failure of the updgrade to iOS 6. Now I am going to have to re-install, organize and set up all of my apps again.