WEBM is video the way browsers like it: open, royalty-free and built to stream. It was born in 2010, Google, out of its VP8 acquisition, and its real weak spot is life outside the browser: editors, TVs and Apple devices get picky.
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.