JBoss EAP 6.4 can be run with JDK 1.8 (that is best and recommended as well, as that is the latest JDK). AS per  JDK 1.8 ** support only with 6.3.3 update and above like JBoss EAP 6.4. So if you are planning to upgrade the JVM then JDK 1.8 is the best suited JDK for you.
 JBoss Enterprise Application Platform (EAP) 6 Supported Configurations
In order to upgrade the JDK all you need to do it to set the JAVA_HOME to point to the correct JDK. For example in case of Standalone mode you can set the JAVA_HOME inside the $JBOSS_HOME/bin/standalone.conf file.
Additionally it is better to not to use JDK 1.7 either (Use JDK 1.8 Only for your EAP 6.4 upgrade path) as it is also older please see the Java SE 7 End of Public Updates Notice: Oracle Java SE Support Roadmap Which says after April 2015, Oracle will no longer post updates of Java SE 7 to its public download sites.