If I knew I was going off and likely to need to split or cut logs that I might want an axe or hatchet. But if I were off without any intent to put myself in that kind of scenario I might want very well want that machete more. I can see any number of jobs that it will do much better than an axe. At the same time, I can see cases when I would want to leave both behind in favor of a strong shovel. If I were on land with lots of grass and no trees, I very well might find no use of the axe.

BMT, part of it is what's right for you and part of it is knowing when to change the gear for the environment and circumstances. I try not to leave without a bottle opener, but when needed I've used a good knife and a set of pliers to open a beer.