I'm a bit torn between a splitting axe and a mace/morning star of some sort.
An axe offers better penetration and is useful for other tasks aswell but perhaps posseses greater risk of getting stuck. A mace is not as versatile but is highly effecive when making direct contact with the skull and is unlikely to get stuck. A mace is also easier to improvise and customize for individual preferences.
A splitting axe doesn't get anywhere near the top. Unless used as a synonym for "axes" in general. A splitting axe is too heavy and meant to be swung vertically utilizing gravity for the swing. You would tire out way too fast using it as a weapon, also vertical swings would have a huge risk of self-injury. A 1-handed axe is probably a much better choice, something like a carpenter's axe or hatchet. This could be in the top 5. If you really want to go two-handed axe, a felling axe is a better choice,
And of course, this takes availability into consideration. Something like a Luctern Hammer or Bec de Corbin would make the list of what's actually better. But unless you are next to a medieval blacksmith, I don't know how you would get one. I doubt the ones in a museum can still be reliably used.
In my view the weight is not so much a factor as long as it's not so heavy that you can't swing it effectively. If you're in a situation that you need to defend yourself with a melee weapon you pretty much only have one chance. If you don't drop it with the first swing you're wrestling next.
You make a good point though. A plain old hatchet will probably get the job done just aswell and trading some stopping power for accuracty might not be a bad trade. I don't think a sledge hammer for example would be any good because of its weight but atleast the Fiskars splitting axe I have is nowehere near as heavy and I can swing it around quite easily.
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