How is it that pistol rounds are bigger than automatic rifle rounds?

The stopping power part all depends on the round used. .223/5.56 NATO has very little stopping power since the round is so light that it gets deflected easily. It also puts a very small hole in the target. The actual diameter of the round is about the same as a .22 long rifle. Now, 9mm is not a very good round to be putting up for pistol stopping power either. The round is pretty small for close range work, whereas a .45ACP round will put someone down quickly. Most people don't get right back up after taking a .45 round to the chest. Some people can take several 9mm rounds before dying. If a crazy person on PCP is running at me, one (or two) good .45 shot(s) will bring them down pretty easily. The same cannot be said for 9mm, but it is possible, no doubts there. I would trust my life in the hands of any good .45ACP pistol over a 9mm any day.