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.
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.