Saws, Axes, Hatchets, Big knives or Tomahawks.

 Saw: these are great for butchering game. Battoning a knife will work, and axes make a mess of things. You greatly benifit from having these for moose, but butchering trees may be different. The reality is that I havent used these in the bush for butchering dead standing for a fire, cover or sleep platforms. My immediae assesment however is  that they seem like more work than the alternative. The nice thing about saws is that they are extremly light as compared to alteratives; they may also fall apart though due to poor construction; but this is true of both axes and knives too. The blade can also snap.

Felling Axes: heavy. You need a horse, or atv to use these reguarly in the bush.

Hatchets: again, heavy to carry on a march. The extra heft may help when butching bigger trees and these can also be used for skinning by using the blunt back to tamp the hide off. 

Big Knives: I have found that something that tries to do everything, does nothing well. But, the hudsons bay company made a knife for the boys outdooors which was quite useful to them, some more exploration is warented. Great for battonning wood, or game. Poor for chopping wood often, butchering, or putting an edge back on due their often heavy girth. Inexperinced outdoorsmen will often choose heavy tools, not thinking much of their weight at the time, only to endure regret later.

Tomahawks: these are my go too. Light. Mine is self made from a cercular saw. They can butcher most trees quickly. A few good whacks on one side and one good whack on the other, or a chew around can make a big dead standing into fine wood to last a couple hours. Paired with a small, light, 1095 useful knife is all you need for all tasks. Im not sure why guys prefer the folding saw over the tomahawk for bush work. 

In a long term, hard use situation, I would not want a hatchent, axe, saw or the tomahawk shown above. Saws blades always break and you need a special tool to sharpen them. Axe or hatchet heads come loose and you need other tools to service them, the tomahawk shown above needs a drill tool to make holes in a new handle, which may be done by making a project of it. 

The tools I would opt for would be a taditional tomahawk or big full tang knife, which is what history also shows was most often used. 

At the end of the day, we use what we have.