The most common riding injury is a broken collarbone or broken wrist, caused by a rider breaking their fall by throwing out an arm. Vests do little or nothing to prevent this, except for the ones that have the extra little shoulder pad over the top of your arm.
Vests do mostly protect your ribcage and internal organs. In high speed falls, broken ribs can puncture lungs and spleens. Vests also do protect your thoracic and lumbar spine from disc or vertebra injury, and from internal bleeding. These injuries are usually associated with higher force and velocity, which means riding at speed or over fences, not just hacking around the ring.
However, if you have a vest, or can afford a vest, wear it and wear it at all times. In all my years of teaching and coaching, the two most serious injuries sustained by my students were spinal injuries (broken lumbar vertebra.) The students were both middle aged woman, who both had soft falls riding on the flat in sand rings. A vest would have saved them both a lot of pain and a long recovery.