The concept behind MUBI is that they provide a small set of curated films which change frequently - sort of like a little independent movie theatre. Criterion is possibly a better offering if you want a large catalogue.
Criterion also rotates through human-curated collections. They do not offer a full library archivally, which was initially a disappointment when I subscribed. It turns out the curated content is great, changes all the time, and really has movies that are worth watching and I don't already know about -- along with lots of favorites.