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 ]
Tomcat is a Web Application Server. WebSphere and WebLogic are full J2EE environments, which must include a web application server. As previously posted, neither is an IDE (Integrated Development Environment), although some IDE's include a WAS (like TomCat) or a J2EE server (like JBoss).
For example, a J2EE environment must include a EJB server, which is not handled by TomCat.
That said, as a designer it is always good to question if you need a J2EE framework, or if a web application server will do. I have often sold management against the need of a a J2EE framework, and instead settled for just a WAS. More often than not, a WAS is sufficient, especially when using frameworks like Spring, which make EJB's unnecessary.
Some questions to ask - what kind of persistence model do you want to support? Is clustering needed? Whats is the failover model for the app?
As a developer, I often develop and test in a WAS, then deploy to WebSphere or JBoss.
Even if the voices <i>aren't</i> real, they still have some good ideas!
Tomcat is a servlet container whereas WebSphere, WebLogic, and JBoss are full blown J2EE / Java EE 5 compliant application servers (which have a bundled servlet container, as well, as an EJB container) within them.
If you are seeking the *BEST* Java IDE on the planet, the one you want is Eclipse.
Its got strong refactoring, unit testing, and SCM support...