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.
I went for a one-handed axe. I don't like a splitting axe because I feel like the primary strength of zombies is the horde, and that a splitting axe doesn't have the mobility to allow you to fend off one threat and then quickly recover and position yourself to fend off another. There's too much momentum in starting a swing, and too much momentum in stopping one if you miss.
There is something cathartic about an overhead swing with a woodsplitter that you pour so much of yourself into that you almost leave your feet, though. When I was younger going out to split wood for the furnace was what passed for mental health care.