Mobx decorates classes/objects/arrays to make them observable and computes derived values from state. The UI then reacts to those derived values. In React Axiom, React components subscribe to models and models publish changes when a model’s internal state changes, then these components access the new state via getters instead of having computed derived values. It’s subtle but important difference to make.
React Axiom is opinionated about how you access/change data from your models (application state), and that is through getter/setter methods. This decouples the data layer from implementation and contains the interfacing logic inside of the model. This also makes stubbing and mocking business logic easier when unit testing components.
Mobx is much larger library than React Axiom (about 9 times). React also only uses ES6 syntax.
There's more discussion here: https://www.reddit.com/r/reactjs/comments/56yalm/introducing_react_axiom_a_way_to_use_models_with/d8o0eff