Tomcat does not support the full J2EE stack (as you know). Just the
servlet and
JSP parts.
JBoss, on the other hand,
does support the full J2EE stack. And it provides the servlet/JSP parts by embedding a copy of Tomcat inside itself. At one time it offered an embedded Jetty option, as well, but I've been told by JBoss people that these days, it's strictly Tomcat.
JBoss is perforce larger than plain Tomcat and has more subsystems to start up and shut down than Tomcat, so you're better off with plain Tomcat is all you ever expect to do is servlet/JSP. On the other hand, when you actually need those other bells and whistles, JBoss is an excellent implementation.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.