I don't think Skunkabilly was very clear about his intended use. "Outdoor use" covers a wide range.
Most people don't get far enough into the wilds to ever need an axe. If you are backpacking, you will likely have no need of either axe or saw. You likely will be cooking with a stove. If you run out of fuel, you can easily cook your meals over a twig fire. My old boy scout manual said if you can't break it with your hands, it's too big for a cook fire. As far as I'm concerned, that's still good advice.
As for keeping you warm, if you travel with a nylon tent and nylon sleeping bag, you won't be doing much sleeping next to a fire unless you want to ruin your gear. So you won't need an axe to chop down the forest for a fire.
I can think of several instances where an axe and saw are ideal.
1) winter camping - if you break through the ice, you need to get a fire going quickly, and big enough to dry your clothes - read Jack London's To Build a Fire
2) canoeing - dump your canoe and you will want a good fire to dry you out, especially if it's late fall, winter, or early spring. Make sure the axe is lashed in so that it can be recovered.
3) It's especially critical if you dump it during a long wet trip because the axe will get you dry wood to get a fire going quicker than anything else. Hypothermia is a killer.
4) primitive camping/hiking - get a good Gransfors Bruks Small Forest Axe - ditch the Gerber - it's junk compared to a GB. The wildlife hatchet is also excellent and the mini hatchet is perhaps one of the best survival tools you can carry and the only one I would choose for backpacking (although if I was younger, I might consider the wildlife hatchet). It has a hammer poll and with a club, you can pretty much get all the wood you want by hammering on the poll to drive the axe into wood for felling or splitting. You should have no trouble using the mini to cut saplings for shelter building.
5) if you are a trapper and spend weeks and months in the wilds, the scandanavian forest axe will build you a small trappers cabin, the wildlife hatchet will make and pound stakes for sets.
There's a lot to be said for building a fire to connect with our primeval past. Like most of you, I have passed many joyful hours sitting by a campfire and watching the burning embers. But if you are in any kind of true wilderness, you shouldn't have any trouble finding firewood for a recreational campfire. If you have to have a chopper to get firewood, chances are you are in an area that has been overused and it would be much better for the environment to skip the fire. Carry a nice planisphere and learn the constellations instead. Fires can isolate you from the night sky.
If you backpack on trails, leave the choppers at home. They just become dead weight and imo, a badge of a rookie backpacker. I do carry a lightweight fixed blade, usually a puukko, mora, or lately I've become enamored of the heavier Gerber Yari. But basically, a good multifunction SAK or multitool will do all the chores you need, mile after mile of backpacking. For protection, I do carry a firearm though. But I've never needed it.