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...
This is an old thread, but in case somebody stumbles upon it...
I have been making many xun, experimenting with design parameters. I am not an expert at playing them, but I suppose I'm decent. Here are my findings:
1) width/height ratio is very important. Taller and skinnier gives increased high range, but decreased sound quality (weak, airy sound). shorter and fatter gives the inverse. W:H of 1:1 gives awesome fat solid sound, but you will struggle to get an octave-and-a-third range. W:H of 1:2 and above will give you octave-and-a-fifth or sixth range but sound quality will be terrible, with screeching and slurping feedback. This is the purpose of 2-chambered xun: the baffle inside eliminates feedback, but does nothing to improve tone. The middle-ground sweet spot? .67:1. This gives reasonably good tone with a reasonably good range (octave and a fourth). This, by the way, is a standard 9-hole xun.
2) Blowhole design is critical. Any xun with a plain hole for a blowhole is garbage. The blowhole must have some sort of bevel cut into the front side of the hole, whether this be a flat or scalloped bevel (scalloped is my preference) This bevel drastically improves sonic response and range. Also, the xun must display some method of allowing the player's bottom lip to come in as close as possible to the blowhole. Some high-quality wheel-thrown xun have a thin vertical lip that forms the blowhole. I build by hand, so I simply cut a scalloped groove behind the blowhole, thinning that portion of the clay body considerably. Getting your bottom lip in close like this allows better sonic response and density of sound.
3) Body composition: I have experimented with low-fire clay and low-fire clay with sand added. Sand-added clay bodies provide a more focused tone. I mix 25% sand with dry clay powder by weight.
4) Body tuning: I have not done extensive testing with body wall thickness, however, I am under the impression that a moderately thick wall (about 1/4 inch or so) is a good thing, provided that it is tuned by thinning a belt around the middle of the bottom half of the body. This thinning removes less than 1/8 inch of thickness but allows the body to vibrate freely, making the xun's sound much more free.
5) Corners kill sound. The body's shape should be as bulbous and organic as possible. This gives a freer and pleasantly windy sound quality.
I hope this benefits somebody.
Edit: after further experimentation, I have learned the huge importance of another variable...
6) Blowhole diameter: The larger the blowhole (and as a consequence, the rest of the finger holes) the more powerful and pure the tone and the greater the volume. The counter-consideration is that the larger the holes, the more difficult it becomes to hit the high range. I feel that a 1/2" diameter blowhole on a 5" tall xun is about right. This produces an addictive power and clarity of tone though it takes some skill and practice to hit the high note on, particularly on the attack.