DbContext global scope vs method level scope

Which version of a class that serves as a data access layer and offers CRUD operations for entities is the best practise in terms of performance in a multi-threaded environment (i.e., methods of this class are called by several threads at once)?

Iteration 1:

Each method shares a DbContext that was generated at the class level.

    class EmployeeService{

     private DbContext db=new DbContext();

     public  Employee GetEmployee(int id)

         return db.Employees.Find(id);
     }


     public void AddEmployee(Employee employee){

         db.Employees.Add(employee);
         db.SaveChanges();
     }
}

Iteration 2:

DbContext is passed with each method call.

class EmployeeService{

     public  Employee GetEmployee(int id){
        using(DbContext db=new DbContext()){
         return db.Employees.Find(id);
        }
     }


     public void AddEmployee(Employee employee){         
        using(DbContext db=new DbContext()){                 
            db.Employees.Add(employee);
           db.SaveChanges();    
        }
     }
}

UPDATE: The question may be overly general in scope, which raises a number of issues.

The interesting part is at how much it costs to create a DbContext object.. Version 2 allows it to be constructed every request, but if it's a hefty object, it's probably best to create a small number of instances and distribute them over several calls (Version 1)