Zero difference. Unless your plugins are compiling code for some odd reason, JDK is redundant to have. JRE - Java Runtime Environment JDK - Java Development Kit The JDK contains JRE and tools so that developers can compile Java source. No server box should need this unless you have applications that compile Java code.
JDK has more tools bundled that you can use for debugging and troubleshooting. Performance wise, there is no difference.