I would like to know are there feature wise same or different? Could you also mention any pros and cons about both of these? Also please mention real-world use case for both Embedded BrokerService vs installed ActiveMQ broker. Thanks in advance!
ActiveMQ is just a Java application, and the embedded version offers essentially the same features as the stand-alone version. In fact, you can configure an embedded broker to take its configuration from an XML file, in which case it will look very similar to the stand-alone broker.
Embedding a broker is a reasonable thing to do if you need the benefit of programmatic configuration; that is, you want to configure things according to rules which are hard to implement in an XML file. It also makes sense if you want close-coupled operation between the broker and the application components, with message data being passed in memory. This might be the situation if you're using JMS as an inter-module communication mechanism within the application.
Embedding a broker has the disadvantage -- and it can be a profound one -- of making it difficult to disentangle problems in the broker from problems in your application. Figuring out the cause of, say, runaway memory consumption could be very difficult. You can get commercial support for ActiveMQ, should you need it, but it will be hard for any commercial organization to support a hybrid broker+application installation.