Pandora on the AppRadio is a built in application. Everything you see on the display is run by the AppRadio completely with stuff like the album art, artist, and track names being read from the phone and then printed on the screen by the built in app. That is why pandora looks and acts differently on the AppRadio 1 vs the 2 and why the apps never get any of the new features that Pandora launches with each of their updates. So how does it work and how has the change to lightning affected it?
The lightning to 30 pin transfers data and the audio but does not transfer video. This does not work for any of the Advanced App Mode apps but it works perfectly for Pandora. The Pandora application normally works by routing the audio from the phone to the radio and retrieving the artist, track and album art information from the USB data port. The data port was also used for controlling the phone. Since the Lightning to 30 pin provides exactly that and nothing more the Pandora application works exactly like it did before.
Now the lightning AV adaptor is different. Instead of audio and data it produces audio and video. It does have a lightning port on it, but that port is solely for power. No data comes from that port. Well that doesn't work for anything AppRadio needs because you need a way to control the actions on the screen. Enter bluetooth. For all Advanced App Mode applications the HDMI port provides the video and audio you see and hear, while bluetooth handles routing the touch inputs to the phone. However like I said before Pandora doesn't use the video signal. It needs the data port to read the information the Pandora app is producing and route that data to the built in app. However again the Lightning AV adaptor doesn't give you data. So bluetooth has to supplement the job of the data port for it. Problem is bluetooth is slow. In my testing I've found its data rate to be about 1-2 Megabits per second VS the 480 Megabits per second transfer rate of USB 2.0. Also anything wireless will lag in comparison to a wired connection. That is why when you open pandora it takes a few seconds for all your artists to load. It is reading the data for the artists from bluetooth which again is slow, but once loaded the app runs the same as before because all animations are done by the Pioneer headunit so there is no lag.
Went a little overboard with the explanation but I hope I cleared up any confusion.
Short version. Lightning to 30 pin does transfer data, lightning to HDMI does not. Pandora needs the former.