Websphere is a full
J2ee Application server
It means all components of J2ee are available in Websphere ,
for instance : EJB stuff
Tomcat is a Servlet container it means that no ejb stuff will operate insde tomcat.
You can use Websphere when you need a reliable high performance full J2ee application server .
but Tomcat is for place where you have no EJB stuff.
Websphere could well integrate with other IBM techs like tivolli , access manager , its EGL ,...
hope it helps