They are supposedly marginally easier to learn to ride that the two-wheeled version and, er, that's about it.
Digging into the memories of a few years ago I had a passing working acquaintance with a local italian who had built a python ("peeton"! It took me all our collaboration to understand what he meant.) trike, perhaps from plans, prehaps totally diy. I never saw it (his home was out in the limousin profond) and he was forbidden to even think of riding it by his close family after he put it in a ditch that might not have been on his side of the road. Pompiers were mentionned in the telling of the tale! He was very taken with the concept, which I didn't know at the time. I think the angle of the hinge is perhaps a bit critical and he didn't get his sums right; it must be one of those things that is dependant on body weight and riding position to remain stable - get it wrong and the beast will never go in a straight line. Difficult to think of a trike being unstable (stability being their principal advantage). The two-wheelers must be real snakes, hissing contempt at all timorous humanoids!
Once you get the hang of the things they work fine, especially in the bits of their home country where a motorway flyover is like unto an Alpine col. We went touring for a few days after the 1990 Europeans with a Native Guide riding a Flevobike with a huge home-built single-wheel trailer. He only touched the handlebars when gears or brakes were required and usually kept his hands behind his head.
Do I infer that the gentle foothills of the Limousin would not be a fitting playground for such a toy?
IIRC, Bikefix's Darth Stuart had one and could ride it proficiently.
I have a set of printed plans that I was given in the mid '90s.
I may be tempted to chop up a bit of steel now that I have a photo or two of the real thing. Can I refer to you if there are any chunks missing in the plans that I have? (I think they are fairly complete)