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JRE Or JDK anything should be fine. You should not face any issue while using JRE to run the JBoss EAP6. As EAP is a java based application server so you can run it with either JRE/JDK. Are youseeing any specific error/warn etc?
Special case with Windows JRE refer to 
jre\bin\server\ On Microsoft Windows platforms, the JDK includes both the Java HotSpot(TM) Server VM and Java HotSpot Client VM. However, the Java SE Runtime Environment for Microsoft Windows platforms includes only the Java HotSpot Client VM. Those wishing to use the Java HotSpot Server VM with the Java SE Runtime Environment may copy the JDK's jre\bin\server folder to a bin\server directory in the Java SE Runtime Environment. Software vendors may redistribute the Java HotSpot Server VM with their redistributions of the Java SE Runtime Environment.
However recommended would be to use JDK instead of JRE because JBoss EAP 6 provides some scripts like "$JBOSS_HOME/bin/jconsole.sh" which can be used to query JBoss EAP6 mbean server instance. Similarly JDK provides some additional utilities like "$JAVA_HOME/bin/jstack" in generating thread dumps and "jmap" etc which really helps in memory mapping for troubleshooting