There is quite a range of tools the fall into the "cleaver' category. I have pictured one here for reference.

I regard a cleaver as a large chefs knife...maybe marginally capable but not necessarily meant to chop through big bones; a bone saw is used for that. A traditional cleaver is meant to chop meat or hard vegetables (like winter squash) against a cutting board, and separate bones at the joints. An ulu would also be used in a similar fashion, but without the offset handle that a cleaver has. There are specialty cleavers made to split deer pelvis, and facilitate skinning and deboning big game animals. These tend to have a more rounded profile.

The cleaver shown here by Ontario Knife Co is a foot long, with 5" hardwood handle, and 7" high-carbon blade. It weighs about 10 ounces, and is a 'steal' at $20.

Compared to a hatchet or a machete, there is much less weight forward. You could lop small branches, but heavier cutting is much easier with a machete or hatchet because of their greater length and forward weight. I also believe that with the lighter weight, slim handle, and wider blade profile, the twisting force of a glancing blow would be more difficult to control. Another concern I have, although I have no proof of this, is that under the stress of chopping in very cold weather, the thinner and wider blade would be more likely to chip and crack.

I am no longer a fan of hatchets, as I have found that they can be very dangerous under cold, wet, and tired conditions (just when you need them the most in a northwoods survival situation). I now prefer a saw and a short machete. I'm sure some will disagree, as everyone uses their tools differently.

I have used several machetes, and can recommend the Ontario CT-1 Camp and Trail Cutlass as a economical (around $25) camp and field cutting and chopping tool, and save the cleaver for your gourmet cookset.