The short answer
Use MP4 for broad compatibility and uploads. Use MOV when staying inside QuickTime, Apple, or camera editing workflows that expect MOV.
Why MP4 is safer
MP4 works across more browsers, phones, social platforms, and upload forms. If a MOV file will not upload or play, convert MOV to MP4 first.
What to check
After converting, review audio sync, orientation, duration, and aspect ratio. Video conversion can expose issues that were hidden in the original player.