I have a few axes and hatchets , and I use them. But, going light in the bush with one main tool, I choose a tough knife that can handle batonning,firestarting duties, jack-of -all trades type of blade. An Esee 5 will fit the bill , and won't fail.
I've done a lot of trips with only a 4-6" blade, and survived just fine. Collecting a lot of smaller wood might be a little more legwork,but I'd rather do that than tire myself out by chopping my ass off all afternoon. I bring an axe when I can , but it usually stays in the truck, not on my back.
It's never an issue of knife or axe with me, as I always have a knife. It's wether or not I decide it's worth to pack the axe too. I bring a splitter axe in the public campgrounds, but usually in the bush, knife only.