In Kansas we don't have a slug season. With the hot, dry weather I don't think they would be out anyway. I don't even know how to clean and cook them, so I just watch TV.
Now that I got that out of my system.......
Slugs are used primarily for deer hunting, mostly in states where rifle hunting is prohibited. The work very well for that, although the range is much shorter than a rifle, 100-150yards at the greatest. Slugs are used as personal defense/home defense and police and military tactical rounds as well, again, very effective as a threat stopper.
Cons, you have to be familiar with the ballistics of the round you are using. How does it shoot from your particular shotgun? What sighting system do you have? Bead sights are dependable for minute of bad guy at up to 75 yards with my short barreled sd gun. Ghost rings, rifle sights, and optics can give you more precision. Slugs can overpenetrate, so awareness of what is behind the target is key. Rifled barrels can give much better accuracy, but sabot slugs that are neccessary cost considerably more.
Hope that helps.