About axes in general, I use one almost weekly at my summer place (a Fiskars splitting axe), and I own a few smaller ones for hiking too (wetterlings, and a mini fiskars). Sometimes its fun to carry one, especially if I know Im going somewhere where building an open fire is not an issue. The largest knife I own is 6" blade, and I find it a bit too heavy and clumsy, so I dont really know about choppers.
I guess it all comes down to what do you want to do, and what do you need to do in the woods. I like camp fires, but for natures sake, I only build one occasionally. I dont use one to keep me warm during nightime (dont need to with modern sleeping bags), and I dont build one every time I want a cup of coffee or whatnot (camp cookers are light and easy to use). Also, even though Id really want to, I dont build natural shelters. Again, tarps are lightweight, easy and quiet to set, and dont require a single tree to be cut down. For these reasons, I simply have no need for a chopper. For emergencies, I prefer to carry a few garbage bags and maybe a space blanket instead of a large knife or a hatchet.
Not trying to preach here, just explaining how I try to do things in this environment.
Now neck knives, those I really like! Im used to carrying my puukko on a paracord necklace; a somewhat rare method in here. Especially with a large backpack, and with a thick winter coat, I find a neck knife a lot easier to access than a belt knife. The knife Ive been using lately is a small classic mora, with 3,5" blade. Its ok for battoning 2,5"-3" thick branches in a pinch.