I don’t have stalls at my farm, so all of my horses are on 24/7 turnout. Have recently had two soft tissue injuries: one a minor strain/tendonitis of the superficial and deep digital flexor tendons in the carpal canal (inside of knee) and the other a tear of the long digital extensor tendon in hock. In both of these instances the vets allowed/recommended full turnout since that is what my horses are used to. The extensor tendon injury was definitely the worse of the two, but the mare is now on month 6 of rest and hopefully will get the all clear to slowly return to work after her checkup next week.
I imagine that stall rest/turnout protocol is really dependent on each individual situation. If you have a horse that goes a bit nuts in turnout and has a serious injury, then stall rest would probably be better for quicker healing. However, I’m a big believer in allowing the horse to get moving as soon as possible, and find that although mine can have their yahoo moments, for the most part they walk around calmly and are much happier being out all the time.