For your example to work, you will need to have a JDK installed and you'll be referencing some EE jars. You don't really need to compare bin folders or anything like that.
In your eclipse environment you'll be setting a couple of things. Your jre should be correct by default so no change there, your project's Java Build Path will need changes though. The build path, you're going to be pointing to some of the jars from the EE installation, such as the servlet-api jar. So that all your compile errors within eclipse are resolved.
What you have to remember is that your eclipse class path is not going to be the same as your deployment class path. For instance, if you want to run your example on
jboss, you'll have to get your servet-api jar deployed to jboss, so it's in the jboss class path. Or if you want to run your example from the command line you'll have to add your jar into the java classpath.
I work a lot with Java EE and I've not downloaded the Java EE. I usually have a specific JDK / JRE installed though. All the Java EE jars / dependencies have been automatically downloaded for me using
maven.
The EE version of eclipse is only going to provide you with some EE development tools. You could do the same development with pretty much any version of eclipse.