The autoresetting breakers are generally used on vital safety equipment that will not do damage if restarted.
For instance, I'm pretty sure that DOT still requires that all headlights use autos. I made the mistake of upping the wattage on my old truck one time, and it was too much for the worn beaker in the headlight switch.
About a mile down the road, they started blinking on and off.
I was able to limp into a late night parts house and buy a new switch. It held for a couple of weeks until I got a chance to add a dual relay with internal resetting breakers.
Fuses are usually required where its dangerous for a piece of equipment to restart without warning.
But, not always. I often work on big motors that have warning stickers saying that it has a self resetting overload and can restart without warning.
Often its just a matter of personal preference. However, the selfies can cause big problems.
A motor that is stalled, and trips the breaker can overheat and burn up or even cause a fire if it keeps getting voltage too often.
The self resetting overloads on a motor are usually mounted in contact with the motor case, and react to both overload and heat.
So, if the motor cannot start and begins to overheat from repeated trying, it will stop trying until it cools off.
Don't forget to consider the third alternative. Manual resetting breakers. They stay off like a fuse, but you don't have to carry replacements.
I put one on my turn signal when it started blowing fuses randomly. It might go months between problems, or happen a couple of times in one day.
The short cleared up as soon as it happened, so there was no way to find it. I mounted the breaker on the dash where I could hit the reset button.
Also remember in general, you can get fuses that blow faster than breakers. So critical current sensitive equipment is better protected.
Just to stir the mix, they also make solid state fuses. They "blow" when they see too much current, and stay blown as long as the overload exists.
When its cleared, they reset.