Compared to EAP 6.1 there are many new features and bugfixes available in JBoss EAP 6.4 that can be found in the EAP 6.4 release notes:
Also you can run JBoss EAP 6.4 on JDK 1.8 (Oracle JDK and IBM JDK) as fully certified JVM. See: JBoss Enterprise Application Platform (EAP) 6 Supported Configurations - Red Hat Customer Portal for more details.
... Additionally If you want to know about the changes/fixes/enhancements/New Features etc... made in EAP 6.2 and then EAP 6.3 and then on EAP 6.4 then you can also refer to the JBoss EAP 6.2 and 6.3 release notes:
If noting else years of development.
But to put it simply JBoss AS 6.1.0.Final is a community release
where Jboss EAP x.x.x is a Red Hat supported product.
from development point of view
AS 5.0 --> AS 5.1 --> AS 6.0 --> AS 6.1.
But after 6.0 was done, AS7 work started from scratch and it was a rewrite of application server.
from there on it went
7.0.0 --> 7.0.1 --> 7.0.2 --> 7.1.0 --> 7.1.1 --> 7.1.2 (where initial fork for EAP6.0.0 happened) --> 8 (renamed to WildFly) --> 9 -> 10 (current)
This are all community releases
EAP 6.0.0 --> 6.1 --> 6.2 --> 6.3 --> 6.4 --> 6.4.x
This are all Red Hat commercially supported EAP releases
In short, beyond the name and both implementing EE6 the two releases don't share much.