I have to agree with Jerry. A saw is a great idea for general use and for survival use, especically if one is not too experienced with axe use, and their hands are not strengthened up yet.

It is very easy to make a survival situation much worse with inexperienced misuse of an axe. If your hands get tired... which they will...and you don't have sufficient skill and experience built up, you may be wearing your axe as a foot ornament.

If you are not experienced with using an axe I recommend getting a saw for the trail and a small steel wedge for splitting. Buy a good quality axe like a gransfors bruks and practice with it when you are alert and not tired from a long trail. Grip it too much and you get blisters, grip it too little and it will glance off the tree and you may be wearing it in the leg. Only once you are practiced with the tools use, should you take it on the trail or put it in your survival kit.

I own a GB forest axe for camping and softwood, and two 4lb old Kelly axes for hardwood use. The major thing that most axes need done to them, is smoothing and oiling the handle until it is like silk, if you use it much it prevents the blisters that a rough handle makes. It is a balance because too rough a finish and you get blisters, and too smooth a finish and an inexperienced user can lose control of it. I wouldn't make the axe razor sharp until you have developed suficient skill to not injure yourself.

All the best with your choosing. It is a persnal choice, most people who are very experienced with axes, want them as sharp as possible and as finely tuned as possible. They also tend to hate poor steel quality in axes.... and knives too, as do I.

Cheers,
Tim.