WMV is a time capsule from the Windows XP years: tidy little files with dated manners. It was born in 1999, Microsoft, and its real weak spot is everything Apple, most browsers, and any phone made this decade.
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.