Yes, you can freely mix both CDI and EJB and achieve some great results. It sounds like you are using @WebService and @Schedule, which are good reasons for adding EJB to the mix.
There's a lot of confusion out there, so here is some general information on EJB and CDI as they relate to each together.
EJB >= CDI
Note that EJBs are CDI beans and therefore have all the benefits of CDI. The reverse is not true (yet). So definitely don't get into the habit of thinking "EJB vs CDI" as that logic really translates to "EJB+CDI vs CDI", which is an odd equation.
In future versions of Java EE we'll be continuing to align them. What aligning means is allowing people to do what they already can do, just without the @Stateful, @Stateless or @Singleton annotation at the top.
EJB and CDI in Implementation Terms
Ultimately, EJB and CDI share the same fundamental design of being proxied components. When you get a reference to an EJB or CDI bean, it isn't the real bean. Rather the object you are given is a fake (a proxy). When you invoke a method on this fake object, the call goes to the container who will send the call through interceptors, decorators, etc. as well as take care of any transaction or security checks. Once all that is done, the call finally goes to the real object and the result is passed back through the proxy to the caller.
The difference only comes in how the object to be invoked is resolved. By "resolved" we simply mean, where and how the container looks for the real instance to invoke.
In CDI the container looks in a "scope", which will basically be a hashmap that lives for a specific period of time (per request @RequestScoped, per HTTP Session @SessionScoped, per application @ApplicationScoped, JSF Conversation @ConversationScoped, or per your custom scope implementation).
In EJB the container looks also into a hashmap if the bean is of type @Stateful. An @Stateful bean can also use any of the above scope annotations causing it to live and die with all the other beans in the scope. In EJB @Stateful is essentially the "any scoped" bean. The @Stateless is basically an instance pool -- you get an instance from the pool for the duration of one invocation. The @Singleton is essentially @ApplicationScoped
So in a fundamental level, anything you can do with an "EJB" bean you should be able to do with a "CDI" bean. Under the covers it's awfully hard to tell them apart. All the plumbing is the same with the exception of how instances are resolved.
They aren't currently the same in terms of the services the container will offer when doing this proxying, but as I say we're working on it at the Java EE spec level.
Performance note
Disregard any "light" or "heavy" mental images you may have. That's all marketing. They have the same internal design for the most part. CDI instance resolution is perhaps a bit more complex because it is slightly more dynamic and contextual. EJB instance resolution is fairly static, dumb and simple by comparison.
I can tell you from an implementation perspective in TomEE, there's about zero performance difference between invoking an EJB vs invoking a CDI bean.
Default to POJOs, then CDI, then EJB
Of course don't use CDI or EJB when there is no benefit. Throw in CDI when you start to want injection, events, interceptors, decorators, lifecycle tracking and things like that. That's most the time.
Beyond those basics, there are a number of useful container services you only have the option to use if you make your CDI bean also an EJB by adding @Stateful, @Stateless, or @Singleton on it.
Here's a short list of when I break out the EJBs.
Using JAX-WS
Exposing a JAX-WS @WebService. I'm lazy. When the @WebService is also an EJB, you don't have to list it and map it as a servlet in the web.xml file. That's work to me. Plus I get the option to use any of the other functionality mentioned below. So it's a no-brainer for me.
Available to @Stateless and @Singleton only.
Using JAX-RS
Exposing a JAX-RS resource via @Path. I'm still lazy. When the RESTful service is also an EJB, again you get automatic discovery and don't have to add it to a JAX-RS Application subclass or anything like that. Plus I can expose the exact same bean as an @WebService if I want to or use any of the great functionality mentioned below.
Available to @Stateless and @Singleton only.
Startup logic
Load on startup via @Startup. There is currently no equivalent to this in CDI. Somehow we missed adding something like an AfterStartup event in the container lifecycle. Had we done this, you simply could have had an @ApplicationScoped bean that listened for it and that would be effectively the same as an @Singleton with @Startup. It's on the list for CDI 1.1.
Available to @Singleton only.
Working in Parallel
@Asynchronous method invocation. Starting threads is a no-no in any server-side environment. Having too many threads is a serious performance killer. This annotation allows you to parallelize things you do using the container's thread pool. This is awesome.
Available to @Stateful, @Stateless and @Singleton.
Scheduling work
@Schedule or ScheduleExpression is basically a cron or Quartz functionality. Also very awesome. Most containers just use Quartz under the covers for this. Most people don't know, however, that scheduling work in Java EE is transactional! If you update a database then schedule some work and one of them fails, both will automatically cleaned up. If the EntityManager persist call fails or there is a problem flushing, there is no need to un-schedule the work. Yay, transactions.
Available to @Stateless and @Singleton only.
Using EntityManagers in a JTA transaction
The above note on transactions of course requires you to use a JTA managed EntityManager. You can use them with plain "CDI", but without the container-managed transactions it can get really monotonous duplicating the UserTransaction commit/rollback logic.
Available to all Java EE components including CDI, JSF @ManagedBean, @WebServlet, @WebListener, @WebFilter, etc. The @TransactionAttribute annotation, however, is available to @Stateful, @Stateless and @Singleton only.
Keeping JTA managed EntityManager
The EXTENDED managed EntityManager allows you to keep an EntityManager open between JTA transactions and not lose the cached data. Good feature for the right time and place. Use responsibly :)
Available to @Stateful only.
Easy synchronization
When you need synchronization, the @Lock(READ) and @Lock(WRITE) annotations are pretty excellent. It allows you to get concurrent access management for free. Skip all the ReentrantReadWriteLock plumbing. In the same bucket is @AccessTimeout, which allows you to say how long a thread should wait to get access to the bean instance before giving up.
Available to @Singleton beans only.
