To transfer data from one system to another, through data interface, by web services, we normally get a result set by SQL query, and format them as a web service endpoint, and allow it to be retrieved by another side.
With EJB 3.0, it seems we can replace the result set by stateless session bean. So are there any advantages over the SQL-based web services? And when should we use it?
This is a very broad question on the system architect level. I will try to answer with my best knowledge without starting a flame war (FYI, I have used both ejb and spring).
As you know, building a stable/robust software application requires many building blocks, such as logging, connection pool, etc. Usually, you can find libraries of these building blocks, but not all of them have common api, so they may require integration. In the worst case, you may have to lock into some vendors. The main idea of EJB 3 (or JEE) is to provide a more complete set of building blocks (via API, annotation or config), so developers can start working on the core business logic right away with an industry standard API/spec/config without training on the proprietary APIs. Additionally, you can change vendor without changing your codes since API/config are really the industry standard (well, your mileage may vary a lot in the real life. hopefully, the new JEE will fix it).
Your application may already have some of the main elements that EJB 3 already provides. However, EJB 3 promises to provide more such as ORM mapping, RMI, Load balancing, failover, transactions, dynamic redeployment, logging, system management, thread managing, resource pooling (db connection), security, caching.
As you have an working application already, you can really consider if it is worth of your efford to migrate your codes to a standard system to gain more functionality vs integrate new functionality individually. Additionally, EJB 3.0 (or JEE) is not really the framework that you can pick. You can also look into other framework, such as Spring.
My suggestion is to really figure what your system requirements, and then pick the right technologies instead of picking up the coolest technologies first.
Good luck