Just a random thought, I'm gonna throw out. As long as the files aren't larger than 4GB you should be good depending on the codec used to encode the movie. I normally don't watch movies on my phone but if I do I always convert them prior.
Try this and see if it plays smooth for you.
1.) Download
Handbrake.
2.) Open app then source/video file and select.
3.) In presets click AppleTV2 (I use to retain 720p)
4.) In Destination name the file and folder where you want it output. Change extension from m4v in file box to mp4.
5.) Uncheck large file size and check web optimized.
6.) Click start and try the file when it's done converting.
Hope this helps,
Mike