The fiskars hatchet is one of my favorites, to be honest. The steel is soft but the thing just seems to work really well.
Here's a video of a guy showing some fighting techniques with a hawk where you can see some of the slicing intents. I think the big thing is the different design of the implement. Some maneuvers that make the hawk supposedly interesting in combat is the penetration with a strong, hacking swing and the ability to hook with the hawk. It reminds me of some of the maneuvers I've seen in karambit videos. It reminds me a lot of the types of things you would do in grappling/ wrestling where there's a lot of actions you could use to throw an opponent off balance to make a more meaningful movement as a follow-up/ combo.
I find them interesting to watch but I don't practice martial arts of any kind so I would stick to street rules of fighting, everything is a weapon and just try to hurt the other person more and hope for the best. Ideally, they would lose interest when they find resistance. I've always considered practicing something like Brazilian ju-jitsu but there's only so much time in a day and there are other things I prefer to do athletically when I find the free time.
I also don't honestly know their effectiveness in real world fighting though my assumption is that a person trained with any weapon is better than someone with a weapon they don't know how to use. This dude in Australia seems like he know what to do with a hawk and has several vidoes on youtube.