How to transfers AVCHD and other videos to iPhone 5S easily: (provided that the output quality could be reserved well.)
Here I take macx mobile video converter as an example:
Firstly, run macx mobile video converter on Mac, added video files to this program;
Secondly, choose iPhone 5S as output directly. You can also crop the video file, extract favorite segment, etc in "Edit" setting.
Last step, begin convert AVCHD to iPhone 5S.

This is my personal experience. Certainly, there are many other software alternative. What's your choice?