What constitutes the 'Woods' in your area. That should help determine your choice of tools...that and what era/style of woodsmanship you're studying...or what you feel like carrying...or whatever.
edit: actually here's a bit more definitive of an answer. I think it is a good idea to have a small knife with you no matter what other main tool you carry, actually the small knife is your main tool and big knives and axes are sort of luxuries. Also IMO if you are not experienced with an axe then low light, tired, end of the day wood processing is much safer with knife and baton. and in that case you should have a saw.
edit II: so, Small Knife, Big Knife, Saw.
or, Small Knife, Saw.
OK OK, Do over: If one was asking whether you should bring a Big Knife or an Axe in when 'Hiking' then I have to assume they are not much experienced with an Axe or Hatchet, because they would know that a big knife is generally preferable only when it is Fun or Necessary. Necessary being only in Tropical/Sub-tropical areas where an Axe tends towards uselessness. I live in the North and have a lot of experience with the Axe, and I find Big Knives to be Fun. But I know that, depending on the Weather or whether I'm in the piny woods or oaky woods that many times an Axe(because I know how to use it safely) will save much time and energy. But you will still often find me, for safety's sake, splitting my small kindling around the fire at night, with a knife and baton.
Please don't mistake my tone for derision, I am totally not trying to sound like that!
Many of those guys have, use, and love BKT and ESEE. It's kind of a knife hippy commune thing
Also I am totally an ESEE Hippy...so Junglas and 4
..and a saw and an axe(if you know how to use it)