I did a riding tour with Cross Country International (now out of business) several years ago; the tour was in southern Tuscany at a place called Il Poggio (you can google it; it's still around). I enjoyed it quite a bit, but probably won't do one again.
My husband and I are not tour type of people, and some of the normal features of a tour type of vacation, I didn't like. Because husband came with, and he doesn't ride, it made more sense to do the kind of tour where you stay in one place, and ride from there each day. The meals were only fine, not great, with somewhat-fixed menus. We go to Italy partly to eat, so it was limiting to us that we couldn't go out to various restaurants (though we did go off on our own two nights). However, the location was gorgeous, the rooms wonderful, and the horses were well-cared for and in great condition.
While I enjoyed riding (I was a low-intermediate rider), I also love lots of other things in Italy, and spending so much time riding meant we couldn't do other things. Obvious, I know, but I decided that I'd rather do a bigger variety on one vacation. Maybe a two-day ride would be better for me!
The terrain where we rode was VERY steep, which I wasn't used to. We mostly walked and trotted, partly because of the terrain. And the steepness was not obvious from the description or pictures of the tour, so I didn't anticipate that. I loved being able to be off in the countryside.
I would assume all of those companies are more like consolidators; they set you up, but everything else is done by the people running the tour incountry. You can book directly with stables in France, Italy, whatever. I might have done that, but I felt as an inexperienced rider, it was best to work with a company that had checked out the operator and the horses.