While the vest will save the wearer the trouble of a penetrating injury it will still allow the bullet to transmit large amounts of kinetic energy(read that blunt trauma)to the body. The amount of the KE transmitted to the body obviously depends on the bullet type, vest type, angle of impact trajectory of the bullet and the wearers body type. With blunt trauma you can have a lot of injuries, such as:
ruptured/fractured spleen or liver
ruptured hollow organs(ie stomach, large/small bowel)
internal bleeding from ruptured vascular structures
pneumothorax(popped lung)
broken bones/ribs(as was mentioned by FFZ)
contusios
pericardial tamponade, the sac surrounding the heart fills wiith blood, impinging upon the heart's ability to refill with, and effectively pump blood
There's so many more,but that's a general idea.
Sherm