Easy way to upgrade from Mandrake to Ubuntu?

Yes, but what about the many other things configured and installed, such as LDAP, DNS, DHCP, MySQL and others.
They and their config files live variously in /etc, /var, /usr and possibly elsewhere.

Presumably one wants the 'new' Ubuntu binaries to overwrite the Mandrake ones, but not to zap the cofig or that data, wherever it is, default or customized.

In addition, I would think that one would want the Mandrake specific tools (the 'drakxxxx' scripts) and their supporting libraries (mostly Perl if I recall) to be removed, since they are redundant with the new Ubuntu tools that will be installed.

So backing up your user data is one thing, but there is a lot of other stuff that represents work done in configuration and data elsewhere.
While normally the Linux config files are better (more readable, comprehensible) than Windows's registry, this is one time that they are a problem.

I do have separate partitions for /home, /var, /usr, /tmp and /usr/local on my Mandrake machine, but it is all these other config and data files spread over them that bother me.
For example, when I downloaded Adobe Acrobat7 it installed in /usr/local. Other vendor specific tings like my printer drivers did too. Guess where Java lives?

Changing from Mandrake to Ubuntu is not simple and is going to require a lot of checking and backing up of specifics beforehand and cleaning out afterwards. Making sure you clean out all of the old and redundant Mandrake stuff and don't delete something from Ubuntu is going to make this painstakingly awkward.