In the last couple years, I have been working with TOMCAT, we always use fat war file, which each web application use their own lib, there are very few library in common tomcat lib directory.
Good: Different application can use different version library, easy to configure, no library conflict issue.
Bad: I guess memory might be a issue. As every web application will start their own version.
Today I check one of the web application implementation in websphere, in web library, there are lot of common libraries.
Good: I guess most EJB related library should be in common.