WHAT'S THE DIFFERENCE?
Quicktime videos generally play well on smartphones and devices that stream video. The quality of the video is lost sometimes when shown on a large screen.
MP4 is the preferred playback format. If you "stream" the file though it can take a bunch of internet resource. It might be best to download the file to DVD or thumb drive and move it to the hard drive of the computer that will be used to play the video during church.