Okay first things first those are GOOGLE PLAY EDITIONS. Basically they are Nexus experience devices under their OEM brandings rather than the Nexus Branding. Google handles the updates for these phones. They do not contain ANY Samsung or Verizon software. The UI itself and all the preinstall applications do not exist on these editions.
Your phone is on Verizon and is a Samsung TouchWiz UI device. When Google releases an update like 4.3 they make the source available to OEM's like Samsung. Samsung will develop TouchWiz back into this new android version. International phones have the least changes of all the varients and they tend to recieve the updates first. Once Samsung FINALLY gets around to updating the Verizon version Verizon will then spend weeks testing it and everytime they have a problem they will reject the build and make Samsung keep working on it. Typically 6 months after a Nexus device gets an update, A CMDA US Carrier variant will get updated.
The Galaxy S4 touchwiz update is expected for October on the International I9505, the exact same phone that is getting this update today will not get 4.3 for another month. Your phone has the same CPU but different radios. Even if you were to successfully install the i9505 Google Play Edition update and come to terms with the fact that you have lost everything Samsung and Verizon about the device. Your Phone, Data and Wifi will not function.