What is the difference between the two? Should that be a selection criterion? What other criteria should I be aware of?
For starters, this site has a varying selection of the Xun. Prices ranging from $23 to $79 US. http://www.redmusicshop.com/Xun
From looking there, other criteria includes the hole count. From reading the wiki and other articles, the first Xun had only one hole but, I assume you don't want to go that traditional? :P The standards today are 8 hole and 10 hole Xuns; the 10 hole Xun also coming with the monikers, professional and concert-grade.
Be sure that the Xun, specifically, is what you are after.
Traditional Chinese musical instruments were classified into eight groups (bayin) according to their materials: gourd, earthenware, hide, wood, stone, bronze, silk and bamboo. It is said that there were more than 70 different musical instruments, but many of them have been lost or are obsolete today. https://en.wikipedia.org/wiki/Chinese_orchestra#The_ancient_Chinese_orchestra
So, it is only a Xun if it is made of earth. As Tetsujin mentions, clay is a form of earth from which ceramic can be made...
Like all members of the ocarina family of wind instruments, its shape has almost no effect on its sound, which has lead to many different forms of the instrument. Some are spherical, while others are egg shaped, flattened or elliptical. Other have the form of a fish or a pear, which is the most popular today and resembles a modern ocarina. https://ocarinaforest.com/ocarinas/chinese-xun/
With this being the case, I speculate that it seems unlikely that the actual earth used to make the vessel would have any effect on the overall tone. You're looking at size and thickness for differences in tone; smaller for higher tones, larger for lower tones.
Also if anything in the composition of the instrument might effect the timbre, it's whether or not the earthenware has been glazed. The glazing itself may effect tone versus a non-glazed instrument. But, glazing is a delicate process in and of itself. Two Xuns of equal size and thickness may sound different due to their respective glazings alone...