If I already had a knife in my survival kit, then the answer is easy....the SAW.
The saw is much more quiet to use than a hatchet, so you don't scare away wild game or attract unwanted attention.
The saw is safer to use:
It's rather easy to injure yourself with a hatchet.
And it's not just maiming yourself that you have to worry about either...you can also injure your back or shoulder or elbow if your chopping technique is not correct.
And the more fatigued and exhausted and weak a person gets, the sloppier and more careless their chopping technique gets.
The saw is easier to use when your strength is already compromised (age, weakness, fatigue, injury, sickness, etc...).
The saw requires less room to use effectively.
The saw needs resharpened less per amount of wood harvested (and you can even carry extra blades since they weigh very little).
A hatchet will dull considerably after just cutting down several hardwood trees, while the saw will keep right on cutting for many many trees.
The saw weighs less and folds up in a more compact package.
The saw can be used much more safely when up in a tree or the edge of a steep hill or cliff.
The saw can even be used underwater if needed.