What are the advantages using LINQ than stored procedure

There are a lot:

1. Debugging - It is really very hard to debug the Stored procedure but as LINQ is part of .NET, you can use visual studio's debugger to debug the queries.
2. Deployment - With stored procedures, we need to provide an additional script for stored procedures but with LINQ everything gets complied into single DLL hence deployment becomes easy.
3. Type Safety - LINQ is type safe, so queries errors are type checked at compile time. It is really good to encounter an error when compiling rather than runtime exception!
4. Built-in security - One reason I preferred stored procs before LINQ was that they forced the use of parameters, helping to reduce SQL injection attacks. LINQ to SQL already parameterizes input, which is just as secure.
5. Reduction in work - Before LINQ, I spent a lot of time building DALs, but now my DataContext is the DAL. I've used OPFs too, but now I have LINQ that ships with multiple providers in the box and many other 3rd party providers, giving me the benefits from my previous points.

NOTE: If all you're doing is simple INSERT, UPDATE, and DELETE statements LINQ is the way to go (in my opinion) and all the optimization is done for you, for more complex work I would say to stick with stored procedures.
For more detailed info, refer this: What is the advantage of LINQ over stored procedures?