Things have moved on in that they've dropped the 2s - it's just JSE/JEE - but I've never paid enough attention to care what those really are.
For desktop apps, I use whatever Eclipse works with by default.
For web apps, I do Railo, which uses a JEE servlet container (Tomcat/Resin/Jetty/etc). No idea if there's any actual JEE involved there though.