
I believe an axe(or hatchet IMO) is only suited for the cabin or your home and only for splitting large logs that have been cut flat with a saw paired with a large, raised, flat stump to place the logs on. In the woods I will always prefer a large fixed blade with at least an 9"(pref 10") blade at least 1/4"(pref 5/16") thick.
Axe:
PROS: Tough to damage(the head anyway) cross cuts better than a large knife(some would say and be wrong IMO) splits wood better some would say(wrongly).
CONS: Heavy, Large size is cumbersome, small cutting surface, not as sharp, dulls faster(tempered softer for impact resistance), not good at all for small tasks(yes I said NO GOOD AT ALL), requires much skill, accuraccy, endurance. Very hard to use one handed(if injured for ex). Even carrying an axe let alone using it in any way uses a ton of energy(not good for the outdoors), if the handle breaks(which I have done) it is now useless.
Large Fixed Blade - A kukri to stick with OP, or even a good large bowie(BK9)
Pros: COMPACT AND LIGHTER WEIGHT, long blade can crosscut a large log(might take longer but will use less energy IME), long blade can split into much smaller pieces and with less energy spent. While maybe not ideal for small chores still leaps and bounds better than an axe or hatchet(try skinning, building traps/snares, or doing any food prep with an axe).
Even carrying a large fixed blade, and a small fixed blade, and a folding saw and a SAK or Multi Tool still is less weight than most axes and supremely more capable.
Cons: More prone to breakage(not likely in most cases, but you'd still have usable cutting surfaces), crosscuts slower(not if you pair it with a saw). Ummmmm........thats all I can think of(and those aren't cons in my book)
But I might be biased...I don't know...
If I missed anything or was wrong in anyones opinion please reply.