xubuntu is a more lightweight and simple version of ubuntu which uses the xfce window manager instead of the default ubuntu one . The window manager is your user interface to the operating system and they can be simpler and do less or more complicated and have more effects and integration.

There are another two distros available. kubuntu with KDE window manager and lubunto with LXDE windows manager. to a question Approximately

Ubuntu is the heaviest and most feature rich followed by kubuntu, xubuntu and lubuntu which is the simplest.

Possible advantages of xubuntu over Mint:

It has a simple interface not unlike win XP. It's reasonably quick on old hardware. It has a basic set of installed software like Firefox, Thunderbird mail, GIMP (like photshop), parole media player - I install vlc as well.

It sounds like Mint is a little bit more user friendly for installing codecs etc.

I'd only go for xubuntu if you find some features of mint too integrated or intrusive and you can't turn them off.

If you download an .iso image and make a bootable USB drive, you can try any of these without installing them and without disturbing your system.

I was just saying that if you choose xubuntu, I might know the answer to any question you might have.