You should use GlassFish for Java EE enterprise applications. Some things to consider:
A web Server means: Handling HTTP requests (usually from browsers).
A Servlet Container (e.g. Tomcat) means: It can handle servlets & JSP.
An Application Server (e.g. GlassFish) means: *It can manage Java EE applications (usually both servlet/JSP and EJBs).
Tomcat - is run by Apache community - Open source and has two flavors:
No commercial support available (only community support)
JBoss - Run by RedHat This is a full-stack support for JavaEE and it is a certified Java EE container. This includes Tomcat as web container internally. This also has two flavors:
Glassfish - Run by Oracle This is also a full stack certified Java EE Container. This has its own web container (not Tomcat). This comes from Oracle itself, so all new specs will be tested and implemented with Glassfish first. So, always it would support the latest spec. I am not aware of its support models.