What a lovely topic! My husband and I currently planning the farm we hope to move to in a year or less and plan to use MIG (management intensive grazing) with a small herd of dairy cows to supply the milk for the farmstead cheeses we plan to make and sell. While we're no experts, we've read a great deal, visited many farms where MIG is implemented, as well as participated in a transhumance.
We spent a week in Abruzzo, Italy this past August with Porta Dei Parchi (Marcelli Cheese), a small scale artisanal producer of Pecorino, Ricotta, and Caciocavallo. We explored the farm for 3 days, making the final batches of cheese for the season, and then for the rest of the week, took their final group of 200 sheep up into the mountains on transumanza where they would stay to graze until November.
These were sheep, and I have not observed a cattle transhumance, so my observations might not be 100% applicable, but just the same... When the animals were en route, obviously, they're constantly stopping in new locations. They're constantly in a tight flock, even when stopped for a long afternoon pause, or for the night, the sheep remained in a relatively dense herd. When we arrived at their final location, although it was wide open meadows as far as the eye could see, the sheep were not left to choose where to eat, each day the shepherd would take them to a new area where they would deplete the forage before returning home for the night to a protective walled shelter (bears have taken as many as 15 of their flock of 800 in one month).
I imagine that, although there is the will of men involved in these practices, that the sheep behave much as they would if they were a wild pack. There is always the fear of predators and the group will stay close together. They say the same was true of the bison in the West of our country. They were constantly in a tight pack because of the threat of predators, they would eat down to the perfect point, the collective mashing of their hooves broke up the hard soil cap, and their manure fertilized the land. Mob grazing searches to mimic this process. Your soil quality and structure will also make a difference on how you dense you would want to graze. In the harder capped areas (dryer areas) you would want a denser grouping, while on softer land, you would want slightly less.
As for free choice, if an animal is left to graze at will, it seems they will eat only what they like and stay away from areas with less suitable forage. This results in a missed opportunity for the improvement of quality forage on your land. When the herd is detained to a portion of pasture, they will eat what they like and also trample unwanted weeds. When left to choose, they will eat down the grasses they like often to the point of no return, where the plant has lost so much of it's root that it will take much longer for it to spring back (when I was a kid, my horse did this in his field and it was a MESS. we had to bushwhack every year and his favorite places were half dirt by the end of the summer).
If you haven't checked it out, Grass Productivity by Andre Voisin, is an amazing book with great insight into this subject -I think you'd enjoy it!
I too would love to hear about any differences in milk quality people may have observed! I think that this too would greatly depend on region.