It appears that the billhook has a stick tang and if so, you may want to take care in how it's used. For instance, heavy chopping could loosen the blade or crack the handle, putting you or another user in danger of injury.
One of my tools is illegal in the UK, so my listing of the tool here, is not a recommendation of use.
At the present time, my chopping tool is a WWII Khukuri and for lite chopping, it is an excellent tool. I have ordered a Wetterlings hunters axe and if and when it gets here, it will replace the khukuri, giving me a tool better designed for heavier wood working and it isn't much heavier than the Khuk.
BRKTs NorthStar is my primary fixed blade. But I also carry a Mora 2000 on occassion and have a Frost SwAK that rides in a bag in the truck. An Eriksson Mora carbon military is on it's way with the axe and will see a lot of use, then will be placed in a ruck.
My "have on me daily" knife is a Victorinox Hunter lockblade SAK w/saw. It handles all of the very lite wood chores and kitchen chores, etc. Many don't like using a folding knife for food duty, but I see no difference in cleaning a fixed blade or the blade of a folder.