I am shooting with iPhone 6 S Plus with image stabilization on and panned footage is smooth on playback in phone but when same footage is in FCP project, and even when it is rendered and shared, the panned footage stutters. Do you have a recommendation as to how to fix the problem?
The iPhone 6sPlus has known frame rate issues. The phone drops frames when recording movement - due to performance problems - and an inconsistent frame rate will cause jerky motion when you drop such video onto a timeline that is set to a fixed frame rate.
Just google "iPhone 6sPlus frame rate drop" and you will get thousands of comments about this issue + some tricks to avoid it.