The resolution of the video exported in Studio is 640x480 while your original footage is 1920x1080 (same with Camtasia). The codec used to export your video is Mpeg4 Visual Standard Profile Level 3 while the codec used by the iPhone is AVC High Profile Level 4.
This is definitely your problem.
Here is the result of my export with Studio 14, using Mpeg2-TS, customized setting, 1920x1080, AVC (H.264), bitrate 15 000 kbps :