You should own both, and be proficient in using both. That includes finding different ways to accomplish things they'd not be normally used for. You may be used to doing something with a knife that would be awkward with a hatchet for example, so you have to figure out a different way to make the hatchet work. And vice versa.
I don't see much point in trying to chop with 7 or 8 inch knives. I would not consider less than 12" unless the knife was something special, and I normally prefer to carry a 14" or 18" blade when woods loafing. I tend to end up cutting brush, limbs, thorns, and saplings more than chop firewood, and knives are better for that. If I planned to mostly deal with solid woods, then the hatchet would be preferred. No, actually, I take that back. If I plan to cut a lot of bigger wood, I bring the chainsaw. But there are times when I might have to clear one tree or limb (like when setting up a deer stand for example) and don't feel like lugging the saw, so usually then I carry a boy's axe. Something with a long enough haft to get both hands involved.
I like my hatchets, and do use 'em, but when I can't really carry both a hatchet/axe and a large knife, I usually just carry the knife. For those of you who also enjoy the big blades, I highly recommend you find a Kershaw Camp 14 (model 1076) before they're all gone, since they've been discontinued. The dynamic balance on this blade is really good, making it very efficient. They must have gotten lucky on this particular model, because the 18" bladed version sucks. The full height flat grind makes it easy to thin the edge to your preference, and the grip is secure. The only drawback is the sheaths will dull the edge (Zytel was a stupid idea for this use), so I stuck a zip tie down in the scabbard to protect the edge. It might be the best $45 I've spent in a decade.