1. Mathesar includes a lot of cool UI elements for CRUD operations on tables, schemas, and columns. Outerbase doesn't have any UI for this, but only a SQL editor.
2. Mathesar has a lot of support for "relationships" (more accurately described as references in Postgres, but I digress) that Outerbase does not. For example, if you're inserting a foreign key column into Outerbase you have to manually type the value of the column you're referencing. In Mathesar, you'll see a dropdown of all the "related" rows and be able to search through their columns to find the record you need.
3. Mathesar is postgres-exclusive, while Outerbase works with many other DB providers.
And more in terms of governance and usage:
1. Outerbase is paid, with a very restrictive free tier. The option to self host is only available to enterprise customers.
2. Mathesar is entirely free and self-hosted.