The D600 can be operated remotely with the new WU-1b wireless mobile adapter ($59.95) exactly like the D3200 - see this demo. The Android app is already available, the iPhone app just got released and can now be downloaded from iTunes:
The Wireless Mobile Adapter Utility is used to establish two-way wireless connections between Nikon digital SLR cameras and iPhone, iPad, and iPod touch devices. Pictures taken with the digital SLR camera can be downloaded to the iOS device, and the camera can be controlled remotely, with the iOS device displaying the view through the camera lens. The file sharing feature makes it easy to upload pictures to social networking sites or attach them to e-mail messages.
- When a wireless mobile adapter is connected to a compatible digital SLR camera, connections can easily be established with the iOS device.
- The camera clock can be synchronized with the iOS device.
- Pictures taken with digital SLR cameras can be downloaded to the iOS device camera roll.
- The iOS device can be used to view the pictures on the camera memory card and add them to the iOS device camera roll.
- The file-sharing features on the iOS device can be used to pass downloaded pictures to other apps for easy sharing.
- The view through the camera lens can be previewed on, and the shutter released from, the iOS device.
- Pictures taken remotely will automatically be downloaded from the digital SLR camera to the iOS device.
Here are some screenshots of the new Nikon iPhone app: