I am currently using DbContext in a Database first situation and it is working fine. DbContext is NOT only for Code First development.
DbContext acts like a wrapper around the ObjectContext. Julie Lerman has a nice explanation, how you can access the ObjectContext that is inside of DbContext here. So if you decide to use DbContext, you can still solve things with ObjectContext if you need to.
DbContext simplifies common tasks. One example is the Find() method.
Product p = db.Products.Find(id);