The panoramas from ICE and Photoshop can be many gigapixels.
In 2011, we saw the Photosynth mobile panorama app released, but because of the constraints of running an interactive shooting mode with 3D graphics, realtime image feature extraction, matching, + tracking, non-stop video display, and simultaneous image saving to storage, the resolution able to be captured is limited, thus limiting the resolution of the final panorama.
With any panorama, the cleanliness of the panorama is dependent on the camera's lens not changing position during capture.
This is difficult with most mobile devices, even when utilizing a panoramic tripod head.
Thankfully (as I'm sure you're aware) the Theta 360's dedicated panoramic lenses are a superior way of capturing panoramas without introducing stitching errors as the only stitching is between the two lenses.