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.
AVI is the veteran of desktop video: dependable in 1995, cranky about everything invented since. Audio Video Interleave: an early container that predates streaming and most codecs you'd use today. That makes it the right destination when what you need is opening old archives and humoring legacy Windows tools.