MP4 is the world's default video: the file that plays before anyone has to think about it. It was born in 2001, the MPEG standards group, built on Apple's QuickTime design, and its real weak spot is very little day to day: as a container its quality depends on the codec inside.
MOV is Apple's homebody: gorgeous on a Mac, awkward everywhere else. The QuickTime container; often H.264 or HEVC, sometimes heavyweight editing codecs like ProRes. That makes it the right destination when what you need is shooting and editing on Apple hardware, where it's the native tongue.