I think this is my first post and I will inject my 2c as I also like Pandora, and would like the best quality possible on my HT.
I have been playing Pandora through a variety of sound systems and different sources: DirectV DVR, ipod, ipad, android, Smart TV, and finally a computer. Except for the computer, I have the other devices hooked up to a full on high end sound system with a Denon HT amp, B&W speakers with sub. The ipod was connected to the HT system via a Sherwood ipod dock. The computer is connected to my office sound system via the built in audio output jacks (nothing fancy there) to the sound system which comprises of a BreathAudio whole house system with an external 200w amp, just to provide background music via rather inexpensive ceiling mounted speakers.
In a nutshell, I think my office system actually produces the best sound from Pandora overall, better than Pandora coming from the different devices hooked up to my HT system. Quite impressively detailed, but of course without the power of my home HT system. My HT sound system is capable of much higher resolution obviously, and components were chosen to favor audiophile sound rather than full on HT.
So, my tentative conclusion from this is in line with what most of you found out: that computer output of Pandora sound is likely of higher resolution than the mobile and set top devices. My HT sound system shows all the sonic deficiencies of the lesser bit rate. I have been trying to figure this out for a while now, and while reading through this thread it makes sense now.
If most of you are correct in reading that Pandora does indeed provide the highest resolution sound only from a web browser or the Pandora One app on a computer, then looks like that the only way to get the best sound from Pandora is to hook up a computer to your sound system. Maybe it is a good way to revive an old laptop or desktop you were thinking of replacing anyway and put to good use, even one of those cheap Net Books. A Netbook would be more ideal I think because of its built in display and smaller size. You may even install one of those "higher end" sound cards or adapters that hook up via USB for even better sound. I think I may just try that right now.
Again, my 2c.