Here are a few Panorama apps which I've tried (aside from Photosynth and Lumia Camera):
Ztitch,
Cycloramic, and
TurnMe Panorama.
While Cycloramic was much anticipated, unfortunately it fell short of "my" expectations. As for the older Ztitch and TurnMe Panorama, they were not as good as Photosynth when I tested them. However, Photosynth also falls short of "my" standards in a Panorama app. All these four apps have one basic flaw - they don't stitch photos very well. You would need to really take good angles and move your camera along a single axis (or a point in case of 360-360 shots).
On the other hand, Lumia Panorama seems to be able to stitch photos better than all those four other apps. The only downside is that it sometimes becomes hard to use it, especially in places where there are not a lot of details for the camera to recognize as stitch points.
So, I guess it's a trade off between ease in taking Panorama photos (Photosynth, Cycloramic, etc. are relatively easy-to-use) vs quality of output Panorama photo (Lumia Panorama, good output, sometimes difficult to use). You could try those other apps and see if they meet your requirements. Let us know what you find.
Edit: TurnMe Panorama doesn't create Panoramas - only a viewer. (When was the last time I used this app?)