I am torn between axe or hatchet, what would you recommend?

The choice between ax and hatchet is a trade-off between weight and utility.

• Axes are heavier to carry, but easier, safer and more efficient to use.
• Hatchets are lighter-weight, but more dangerous and more tiring to use.

My advice is to make the decision based on how far you will have to carry the tool.

If you are car camping (IE camping within a short walking distance of your car so you can make multiple trips to bring in all your gear), either tool is reasonable. The ax is more functional, so choose the ax if you won't mind carrying it the distance from your car to your camp. When making the decision, keep in mind the amount of other gear you have to carry, and how many trips it will take. Also keep in mind your personal safety when carrying a sharp tool; make sure you can carry the tool in such a way that if you slip and fall you won't cut yourself. A sturdy blade cover/sheath is a good idea for longer hikes.

If you are backpacking, no amount of increased utility can justify the added weight of the ax. It's also quite difficult to strap such a long tool to a pack, so you might have to carry it in your hand the entire time. By the end of the day, you might not have the hand strength to wield the ax safely. If your ax doesn't have a sturdy blade cover, there's the added danger of carrying an exposed blade all day.

A hatchet can be a reasonable tool to bring on a backpacking trip if you plan to do a lot of wood chopping. If you're hiking in a group, it can be worthwhile for one person to carry a heavier tool for the benefit of the whole group. A blade cover is an extremely good idea, so you don't accidentally cut yourself or your gear. My partner used to carry a hatchet on our two-person backpacking trips. Eventually he decided that even though a hatchet is nice to have, it isn't worth the weight (about 2 pounds). Now he carries a substantial knife that can be used for splitting wood by the batoning method, while I carry a saw. He still says, "I wish I had my hatchet," at least once per trip. But he hasn't gone back to carrying it because it's not worth the weight.

Personally, I usually take neither. Instead, I bring a sturdy knife and a saw. The knife wouldn't be replaced by hatchet or axe: it is anyways needed for cooking and it is at least as good as a hatchet/axe to make kindling (if I cannot collect that directly, anyways). The saw weighs less than a hatchet and sawing is more efficient than cutting by axe for all but the comparably narrow range of diameters that is too thick to break but can be chopped off by a very few blows.

Hatchets and short handled axes such as in the linked post are rather accident prone as tools go: hatchets for the other hand (when splitting wood) and the legs, short axes such as discussed in the link more for the legs and possibly feet. These kinds of accidents are no good at any time, but they are among the really bad category in the outdoors.

Axes with a handle length above 90 cm (maybe already 80 cm?) or so are much less dangerous since you'll reliably hit the soil in front of your feet. They are also more efficient in what you can cut and split with them. But they are not the size one carries around on a camping tour unless the plan is to make a long-term camp in one spot.

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For making shorter pieces of wood (which is the main "mode" of cutting wood I encounter during camping), the diameters suitable for efficient cutting by hatchet can usually also be broken. This requires finding/building a suitable leverage counterpoints whereas working with the hatchet or a short axe needs a suitable chopping block. Where I have been so far, the former is usually quite easy, the latter is doable as well if one considers working with the hatchet while sitting on your haunches.

For car camping, I've been using the bumper (used to have a light truck that had a square pipe of several mm wall thickness as rear bumper) and trailer hitches as leverage points.