Not sure how a chopping knife, a machete, and an axe can really be compared.
If I was in a Scandinavian forest I'd want an axe and not a machete. If I was in the Amazonian jungle I'd want a machete and not an axe. If I am in my backyard in the Rockies I want a chopper instead of the other two, except for when I want one of the other two and have to go in the house to get it.
Not sure if that answers the OP's question but that's how it works for me.
I understand the value of specialized tools, and I own and have used all three of these tools (although in the original post, I wasn't asking abot axes, I was comparing machetes and large knives). However, usually on backpacking (and also in a survival situation), I want to pack lightly and minimally--I don't want to bring all of these tools. And in a typical backpacking or survival situation, I want the tool that is the most VERSATILE for the widest array of tasks that I do, while also being safe to use, and light/compact enough to carry. If I knew exactly what I was going to run into, I could always bring the perfect tool (an axe, or a machete, or a large knife, or a shovel, etc.). But because I have weight limitations to what I can carry, and don't always know what I'll run into, it makes sense to bring the one tool that is able to do the widest range of tasks, and also to do well at the most common tasks that I need it for.
My hunch, is that either the machete, or the large knife come the closest to being this multipurpose tool for me. And I think that has kind of been confirmed in this thread. The axe has a place for certain kinds of uses, for instance, if I were building a more semi-permanent wood shelter, or clearing a large forested area by hand, I'd want an axe for sure. However, for handling a wide variety of backpacking/survival tasks with one tool, it seems hard to beat a machete or a large knife for versatility. The machete guys on this thread have convinced me that the machete--if you have a quality one and a good blade grind--probably wins even over the large knife in overall versatility. A properly sharpened large knife may be a LITTLE better at certain things--possibly at splitting wood, and definitely at detailed carving tasks--than most machetes, and it's usually going to be more portable well.
Bottom line: I'll probably keep my Junglass, because I can still see cases where I'll want it and it's more compact than most machetes. But at the same time, I'm going to start taking my golok on backpacking trips when I can, get it sharpened up better, and learn to use it for more tasks, and see to what extent it can compete with or even outdo the Junglas.