davout,
The behavior is intended as the JEE libraries are almost always part of the server environment in which you deploy your application. Even when deploying from MyEclipse directly, we do not deploy this container, those JARs will be provided by the server.
As far as the difference in the two export operations is concerned, the WAR (MyEclipse) option is specifically written by us for use in Exporting MyEclipse web projects. The other one comes from the Webtools project and can be used in case you have WTP web projects. These two will be consolidated in MyEclipse 11.0.