It depends a bit on where I am going.
If it is just for a hike on a wilderness trail a can of bearspray is good to have.
If it is for working in an area which is pretty sure to have bears or big cats, then a rifle or shotgun in the hands of somebody who knows what they are doing is better.

So If I was going to be working around a dump or in the middle of a seasonal food source I would consider firearms.

Cougars are still very rare and the odds of getting attacked are very low. Cats do tend to be attracted more to children because they see them as easy prey.
With cats the young males are driven to locate a new territory and establish themselves. Since a cat covers so much area this often drives them into contact with humans.
These young males are not familiar with humans and don't fear contact quite as much as they should
That also makes their attacks kind of random.

All good reasons to never let kids out of your site in wilderness areas, but even in developed areas cats have been known to appear and attack.