For your use case where the application runs on one server and the database runs on another, the choice between EJB and Spring is irrelevant. Every platforms supports this, be it a Java SE application, a simple Servlet container like Tomcat or Jetty, PHP, Ruby on Rails, or whatever.
You don’t need any kind of explicit remoting for that. You just define a datasource, provide the URL where your DB server lives and that’s it.
That said, both EJB and Spring Beans do make it easier to work with datasources. They both help you defining a datasource, injecting it in beans and managing transactions associated with them.
Of the two, EJB (and Java EE in general) is more lightweight and adheres more to the convention over configuration principle. Spring requires more verbosity to get the same things and depends a lot on XML files which can quickly become very big and unwieldy. The flip side of the coin is that Spring can be less magical and you might feel more in control after having everything you want spelled out.
Another issue is the way EJB and Spring are developed.
EJB is free (as in free beer), open-source and non-proprietary. There are implementations of EJB being made by non profit organizations (Apache), open source companies (Redhat/JBoss) and deeply commercial closed source enterprises (IBM). I personally would avoid the latter, but to each his own.
Spring on the other hand is free and open-source, but strongly proprietary. There is only one company making Spring and that’s Springsource. If you don’t agree with Rod, then tough luck for you. This is not necessarily a bad thing, but a difference you might want to be aware of.
Doing everyting @Annotation is always good? configuration never needed?
It’s an endless debate really. Some argue that XML is hard to maintain, others argue that annotations pollute an otherwise pure POJO model.
I think that annotating a bean as being an EJB stateless bean (@Stateless) or a JPA entity (@Entity) is more cleanly done using annotations. Same goes for the @EJB or @Inject dependency injections. On the other hand, I prefer JPQL named queries to be in XML files instead of annotations, and injections that represent pure configuration data (like a max value for something) to be in XML as well.
In Java EE, every annotation can also be specified in XML. If both the annotation and the XML equivalent are present, the XML overrules the annotation. This makes it really convenient to start with an annotation for the default case, but override it later via XML for a specific use case.
The current preference in Java EE seems to be more towards (simple) annotations combined with a large amount of convention over configuration.