Upgrading is different on every operating system because each operating system has its own package management system. So far, there's no multiplatform open source package manager. Surprisingly, there has been little or no effort from the open source community to make it easy or reliable to upgrade Tomcat.
On page 56 in our book, the section named Relocating the Web Applications Directory shows how you can keep Tomcat's distribution files separate from your webapp and custom config files. This is helpful if you want to upgrade Tomcat, since you can install multiple Tomcat distributions and simply point the scripts to
the distribution of your choice by simply changing the value of the CATALINA_HOME environment variable.
If you're running Linux, you can use the jpackage.org Tomcat RPMs:
When new versions of this package come out, you should be able to use RPM to upgrade to the newer package. This RPM package has some limitations, however. For example, the init script has an unreliable restart function, and the RPM package installs Tomcat in the /var directory (not where most people want it to go), and it's not a relocateable RPM package.
I hope this helps!