Advantages for Stored procedures:
More easily code reviewed.
Less coupled, therefore more easily tested.
More easily tuned.
Performance is generally better, from the point of view of network traffic - if you have a cursor, or similar, then there aren't multiple trips to the database
You can protect access to the data more easily, remove direct access to the tables, enforce security through the procs - this also allows you to find relatively quickly any code that updates a table.
If there are other services involved (such as Reporting services), you may find it easier to store all of your logic in a stored procedure, rather than in code, and having to duplicate it
Disadvantages:
Harder to manage for the developers: version control of the scripts: does everyone have their own database, is the version control system integrated with the database and IDE?