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.
MKV is the format that hoards: video, a dozen audio tracks and every subtitle, all in one box. The Matroska container: it will hold practically any codec ever made. That makes it the right destination when what you need is high-quality rips and archives with multiple audio and subtitle tracks.