1. Get results for multiple queries at once. A simple example would be SELECT 'hello'; select 'world'; which will return two result sets, where base will only return the first one.
2. If your select query contains a tables primary keys, then the results from a query can be edited inline. Example if you run SELECT * FROM myTable WHERE id IN (1,2,3) then you can actually edit the results directly without needing to switch back to the data view.
3. If you have a trigger or view that depends on a specific column or table, and the column/table gets renamed, SQLite Professional will prompt you with the details and alter the underlying trigger/views to be updated with the new proper information.
4. SQLite Professional will automatically reload if your database is modified by an external app (such a directly via a sqlite3 prompt, a php script, etc).
That said, Base is a great app. If you already own a copy of it and the above functionality does not interest you, I would probably just suggest keeping with it.