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 for churches and large gatherings. If you "stream" the file, it can take a bunch of internet resources. It is best to download the file to a DVD or thumb drive and move it to the hard drive of the computer that will be used to play the video during church.