Hi PanzerMike, the advantages of Steam are that when you save your games, if you use a different computer sometimes, the same saves will be available for you (Steam Cloud). I have a laptop upstairs and a desktop downstairs, so it's a convenient feature to have--especially if you travel.
Also, patches should be automatically updated instead of having to search for them and download them manually.
Regarding the beta patches, I guess it's up to the developer, but usually on Steam, if you go to the properties of the game (right click), then beta versions can be available if the developer makes them available on Steam.
And yes, you can absolutely still have the Matrix version and the Steam version on the same computer.
Other than that, I don't know of any other differences.