I believe that there are no mechanical differences between the 2012 and 2013 models. It is my understanding that the only difference between the 2012 and 2013 Genesis Rspec is the navigation system and the ability to stream music wirelessly through Bluetooth. Also, there have been multiple reports (and posts on here) about excessive oil consumption on some 2012 Rspec 5.0 liter engines, but from everything I have read, Hyundai rectified that problem for 2013.
I own a 2013 Rspec and have had no problems with excessive oil consumption. I owned a 2009 Genesis 4.6 with the technology package before I purchased my 2013 Rspec. The navigation system in the 2009 is EXACTLY the same as in the 2012 Rspec. So let me explain the notable differences:
In the 2012 Rspec, the navigation system has, as I said, the exact same buttons and interface as all Genesises (yep, that's how you pluralize Genesis) with the technology package from 2009-2012. In 2013, Hyundai rolled out an updated "Ultimate Navigation" system with a bunch of updates, which my 2013 Rspec has.
This includes added buttons around the DIS control knob, a slightly different control knob (which, I think, added plastic to the grip and makes it look cheaper than the previously solid-aluminum knob), an updated radio interface on the screen, and redundant radio controls on the dash just below the navigation screen. You'll notice in a 2012 or prior Genesis, the only thing below the navigation screen is a CD slot, a volume knob, and a button to eject or load CDs (that's what my 2009 had).
In 2013, they added redundant buttons that include radio seek/track up and down, AM/FM button, satellite radio button, a media button, and a physical tuning knob. Also, for 2013, they added the ability to download music, movies, and photographs directly onto the car's hard drive. Because they added the ability to download and store music, for 2013 they deleted the 6-DVD/CD changer in lieu of a single disc CD changer.
I do notice that the overall screen color in my 2013 is a light brown, whereas my 2009 was a light blue. Some of the menus are also different than in my 2009. And as I said earlier, for 2013, you can now stream music wirelessly via Bluetooth with the technology package.
Finally, the 2013 navigation system is able to be updated by the owner of the vehicle by purchasing a USB/flash drive from the navigation company, MNSOFT. I've already updated my navigation system and it took a little over an hour.
With a 2012 or prior Genesis with the technology package, you MUST take the car to the dealership in order to have the navigation updated. From what I've read, it takes about 6 hours and costs A LOT of money depending on what dealership you go to.
An owner cannot update the navigation system himself. Other than all of this, I do not believe there are any other changes to the 2013 Rspec. And, for what it's worth, the only difference with the final 2014 model (before the complete redesign) is a heated steering
wheel in US-sold Rspecs. Let me know if you have any other questions.