In handlebar terms, I liken it to the difference between simply placing your open hands on the handlebar vs actually gripping the bar with your fingers and thumbs. Or the difference between wearing slip-on style flip flop shoes vs. lace up shoes. Which scenario would you have more control over?
I initially switched to clipless as a mountain biker, because my feet kept slipping off the pedals on rough terrain. Not having to mentally think about and physically keep your feet perfectly positioned on the pedals, allows you to concentrate on other things. I crash much less since switching to clipless, because I have more control. Years later when i began road biking, it just seemed natural to also use clipless on that bike.
All that being said, I have flat pedals on my cruiser bike because I don't want to deal with wearing special shoes for neighborhood jaunts. There is something great about jumping on a bike and just riding, without worrying about all the "accessories" of a modern cyclist.