MOV is Apple's homebody: gorgeous on a Mac, awkward everywhere else. It was born in 1991, Apple's QuickTime team, and its real weak spot is traveling: Windows, Android and the web would all rather meet an MP4.
FLV is a relic of the Flash era: the format YouTube grew up on, stranded when Flash died. The Flash Video container, typically holding old H.263, VP6 or early H.264 streams. That makes it the right destination when what you need is nothing new: today it's mostly old downloads waiting to be rescued.