Clint Smith of Thunder Ranch is one of the most highly respected trainers in the industry. In the NSSF video below, he discusses the use of a pistol versus a shotgun for home defense.
Often, the shotgun is downgraded as a home defense tool due to its length and the thought that an intruder could grab the barrel. As Clint shows in the video, the difference in length between a properly presented handgun and a shotgun is not that great. That said, regardless of the weapon used, you need to train as Grant Cunningham makes clear in this post.