Are talking axe, hatchet, or tomahawk?

And knife, or machete?
Anyways when I go on extended trips I tend to take a machete for soft smallish green wood, a saw for cross cutting larger dry logs and a junior/youth axe for splitting. That said I have been meaning to try a smallish 'hawk style axe to cover more of the machete and axe side of things, and maybe the large camp knife bits too. I don't see why a properly designed head wouldn't work well at those tasks, processing game, as well as wood prep and clearing.
The flip side is a large knife to cover those tasks too... I know how effective a machete is and I can see a large knife in premium steel being even more effective, but handling for finer tasks may be trickier as it gets larger.
I think the real difference is not whether certain tasks are possible with either, but the effort required with where they differ. Is it better to get the speed and length with a handle or with a blade? Is it better to have the easy swing all the time or to use a local log to baton with?
These are things each of us can only answer for ourselves and our preferences. I like low effort and low carry weight, thats why I carry a portable saw. It gets me the most wood with the least effort.
Which are you more likely to hurt yourself with? This is critical for those of us who do the backwoods stuff alone. Safety matters more there. What woudl be a minor inconvenience at home can be fatal in the backcountry alone.