AVI is the veteran of desktop video: dependable in 1995, cranky about everything invented since. It was born in 1992, Microsoft, and its real weak spot is modern life: no proper streaming, no subtitles, no love for modern codecs.
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.