I too like a convex for most work with a bill hook (or a reduced shouldered scandi with secondary bevel... a poorly radius-ed convex?) - I usually tickle the edge up with a butchers steel after heavy use and keep it paper slicing sharp.
At the Care Farm I work at the bill hooks all seem to be maintained to retain a saw edge with nice rounded edges between the blunt "teeth" ... the edge is cared for by smashing them through the nails in the pallets that are chopped for kindling and/or using H girders as chopping blocks.
The staff need as much training as the participants when it comes for tool maintenance...
I spent a whole day fettling the billhooks and hatchets, took one bill hook home to make a new handle (the half tang had been smashed through the hickory by someone using the back of the blade as a hammer - the pin through the ferrule had made a great pivot...) hours of work that could have been avoided with a bit of common sense from staff...
Not all folk understand tools... no matter how good they are as care and support work