Honestly, I seldom carry a saw or axe. Having the right type of belt knife might just make that unnecessary. However if you are set up in a remote area and plan on being there for an extended period of time then to not have one if not both of these tools is planning to do things the hard way.
I own a bow saw or two, a Hudson bay axe and a stout hatchet. All seldom used.
Fixed Pruning Saw
Small Bow Saws
If you have ever seen any of the old outdoor life books printed for the outdoors men of the 1950's you'll notice that there was always some Norman Rockwell type picture on the cover of a white man with hat tipped back on his head plaid shirt selves rolled up (as well as pant cuffs..whats with that?)
and holding an axe........was this guy a hunter? a camper? Lumber Jack?
I'm not sure but one thing was certain, outdoors men carried axes! youbetcha!
It was just the way things were back then, trees were always going to be in our great forests and in enumerable amounts so chop away old boy, build that fire or fence or cabin, lake side dock, tool shed to keep your axe in.
Today we know that was a dream that could not last. Trees like people need space and when people need more space the trees suffer first. felling trees is just unnecessary and wasteful to the causal camper. It should never be done.
My favorite "large" tool is the pruners saw. If I must use wood thicker then my belt knife can handle then this saw does a truly excellent job. 
Inexpensive to boot.
Lite and portable and can cut through a six inch log without too much effort.
I, like most outdoors men today visit the wilderness, I don't live there. I don't need "permanent" shelter. I wont be building corals for live stock or a barn for feed, my axe is seldom used. Even the Hatchet has seen little use but I own them and know how to use them just in case.
We are taught to make efficient and economical fire sets when ever we camp. We use the same fire rings whenever possible and only use wood from the forest floor. This is a long way indeed from our axe toting friend on the cover of the book. We love and enjoy the forest as much as he ever did but we understand better now that these things are finite and we are the stewards of the forests and all wild places.
Big tools have their place, have them and learn how to safely use them in case a survival situation presents itself and you must build (semi) permanent shelter. For week end camping or two week vacation along the A.T. perhaps...leave em home.
On to the Survival tool. I hesitate to call these things knives, their just too big to be a knife.
When Crocodile Dundee said "Now that's a knife" he should have said "Now that's a big heavy chopper/cutter misfit of a tool". These things are small wonders and practically useless all at the same time. Too big to be a knife too small to be an axe/machete. In its search to be all things it does none of them very well.
In the movie CASTAWAY, Tom Hanks opens coconuts with an ice skate....Kool.
I guess I would too if that's all I had (with my luck, I'd have roller skates) but that's just the way you should look at survival tools.....not as good as the tool you should be using but it's all you have.
Sawback on the Ontario
Ontario Survival Machete
I've never seen one with a sawback that was worth a damn, yet they all tout the uses of the survival saw........poor designs at best. The Bowie styles are not bad for chopping under brush or killing hostiles but useless for real work. The thick and heavy slab sided ones claim to be good for prying and digging......not! they are too short or brittle for both jobs, like the Bowie they do one thing well.....chop!
What makes the perfect survival tool? Easy answer, it doesn't exist.
In order for you to have the perfect tool you would need to know what the terrain and vegetation was in the area you're traveling.
(Guatemala = machete / Canadian Rockies = axe) it's hard to say but what I can say with certainty is no one tool will ever do it all.....at least not well.
It turns out that the best BIG tool may not be a big tool at all. If you know what you're doing you can use a "Tool Seed".....
A WHAT? A tool seed is a tool that makes other tools. The Swiss Army knife for instance is a tool seed. It does some jobs itself but can aid in cutting, clipping and bending other things into tools. Didn't you ever see Macgyver ? Swiss army knife and some steel wool and he'd make you a Coffee pot or a Volvo or a helicopter or a time machine...........whatever.
You understand.
Swiss Army
Leatherman Multi Tool
Today we have the Multi tools....The Leatherman tool will go down in history as the tool of the working man, knocking the Swiss Army off it's pedestal forever.
The modern survival tool from which other tools come......................
Safe Travels
RJ
