A Matroska file of the same size will be of a little higher quality because of less overhead than AVI. The main difference in quality however comes from the format of video and audio.
In Matroska you can store just about any of the popular video and audio formats. You don't have to use AAC just because you would like to use AVC but the MP4 does't support your audio format. Matroska also offers an official way to describe each stored track, so that you know the langage and can identify Director's Commens prior to listening.
My personal opinion: Matroska was designed as a container for videos "backupped" by users and serves this purpose best. Other containers were created either for streaming, or commercial purposes.
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