Get the one with a circuit breaker
Yes, they’re safer, and you should use them for anything with a motor or a heating element.
A built-in circuit breaker (also called a GFCI in some cords, but that’s different—a breaker protects against overload, GFCI protects against shock) will trip if the cord starts drawing too much current. That means it’ll cut power before the cord overheats and starts a fire. A plain cord just sits there and melts.
Use a circuit-breaker cord for space heaters, air conditioners, power tools, or anything that pulls a lot of amps. For lamps and phone chargers, a basic cord is fine. But since the price difference is usually five bucks or less, I’d just buy the safer kind for everything.
Future you will appreciate not replacing a melted cord.