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Short answer, take both and a folding saw.
There's lots of variables to consider here, there's no one easy answer. Fixed blade, how long, 12" chopper or belt knife? With a 4" or so blade, you won't have the chopping power of a hatchet, but you can baton. If your hatchet is really sharp, it can still do some knife jobs. I've gone to the woods with all the above, just a multitool, and everything in between. I've made due with each situation, sometimes wishing I had a different tool. In the desert the wood is so dry that you can just snap it over your leg, but not all places are like that.
What's the AO, how much wood will you need for a fire, for a shelter, is it wet? When the only wood around is a downed tree, you can limb it, or maybe you'll have to cross cut through the trunk many many times, then split those pieces, you'll wish you had a folding saw and the hatchet. That's what I've found to be true. I've had nothing but wet wood on the ground, but a downed tree was dry. I wish I had the saw that day, all I had was a 12.5" chopper, it worked, but it was a workout. My new Silky Gomboy would have made that process much faster.
I take many tools these days, the saw, the belt knife, and some sort of hatchet, hawk, or small axe.
I have almost always taken a hatchet/axe of some sort and a folding knife with me when camping. I don't subscribe to the batonning Fad, so I've never really had to do anything with a fixed blade that I couldn't accomplish with a folder.
Saws are just the cat's pyjamas, though, definitely bring one of those if you're going to be cutting wood, regardless of what else you choose.
Why am i going into the woods?
I Donno, to take a dump?
Why would I need EITHER tool for such an expedition??!!! I'll take toilet paper, and lay off the high fiber
But if the question is which do I take into the woods, my answer is knife - rarely am I in the woods and require a hatchet, whereas I often require a knife. I would only carry a hatchet if I thought I might need it for a specific purpose where in my hands it would perform better (more efficiently) than a knife, and those purposes are few.
Solved! I'm getting an estwing hatchet for Christmas and I have a 1/4" thick fixed blade antique custom I pulled outs the drawer. Has an original convex and a real stag handle.