I almost always prefer a hatchet to a big knife. To me, it is just more versatile.
When assembling my trio off tools, i do so with this in mind: If for some reason two of my tools get lost or broken, i would like to be able to survive with whichever i have left. If i loose my hatchet and fixed blade, i can get by pretty well with just the SAK. If i loose my axe and SAK, i can do fine with just my fixed blade. If i loose my SAK and Fixed blade, then i will be just fine with my axe. Looking at a large fixed blade as a singular tool, I dont see it as beeing all that usful.
I am pretty well versed in the usage of an axe, and feel that with it, i can do most things, including fuzz sticks, notching, whittling and such. but that is just me personally. plenty of people couldnt do any of those things with an axe, just as i can hardly do them with a big knife.
if weight is an issue, i would just opt for a saw. really, you never need to do much chopping or hewing unless you are doing some sort of timbercraft (yes, i just made that word up i think). a saw will get it done alot of the time, and, as jake said, it is usually safer and more compact.
in a differant enviroment though, other things might work better. in a jungle, a chopper would be rather cumbersome, as would an axe/hatchet. a machete is obviosly much more suited to this enviroment. An i dont really lump machetes into the chopper/big knife categorie.
so yea, it just depends.