A billhook makes for a sturdy cutting tool, whilst it is typically used as a hacker / slashing implement I regularly use mine for making kindling, log chopping & have found it good enough to quickly lop a 35yr old tree where a chainsaw wasn't an option.
In fact it's such a common item for agriculture out in the 3rd world (still) that this itemwas probably responsible for many thousands of lost limbs in the Tutsi / Hutu uprisings back in the 1990's ..sadly.
Therefore a must have for any zombie kit, but more likely tremendous potential to off a burglar realistically.
If kept sharp this will often prove far more useful than a hatchet, ..I don't go to the woods without one (bushcraft).
Balances better in the hand (& therefore the action of cutting) than a hatchet, with a bit of practise it makes for a very effective thinning tool as you can go all out with it or merely cut slivers..
As with any "chopper" look up & learn the invaluable use of the "cissy stick" technique, it' will save your fingers without slowing you down!
Incredibly versatile, why don't you have one yet?