Finally had to weigh in with some thoughts.
After reading this, I realized that we do not all have the same definition of "big knife". If you consider a 9" blade big, then yeah, a hatchet will probably outchop your idea of a "big knife". Here's my big knife.
If you need to chop a lot of bigger wood, then a hatchet will serve you better. If you're clearing very light succulent vegetation, like nettles or something, then a long stick is a better solution than any machete. If you're clearing light but tough vegetation, like brambles & tufts of fescue, then a light & quick machete will serve better. If, like me, you find yourself clearing tough undergrowth and smaller trees, (up to about 4" dia trunk) then my Bowie is the best compromise I've arrived at. It's faster than a hatchet, carries through better than a machete, & does everything a 9" blade can do. Comfortable carry is more a function of the carrying system (sheath/scabbard) than the object itself.
In regards to use as a weapon: Someone mentioned the hatchet having a mightier blow than the big knife. Again, if you're talking about an 8" blade, then yeah. But I'd choose my big Bowie over either one.