Your question is not clear. Are you asking about IDE or about server?
Apache Tomcat is a web server. It is not an IDE. One open source IDE is eclipse.
IBM Websphere is a brand. There are many products under WebSphere brand. You may be referring to WebSphere Application Server and Weblogic application server. The work, for which Apllication server is required, cannot be done by web server.
[ October 02, 2007: Message edited by: Sachin Vrma ]