So to tie this up in a pretty little package, an 18-24" Splitting or chopping axe would be your choice for a rig/camping tool?
You either get a splitting tool or a chopping tool Either can do both but not well. To split you want a wide heavy head, that doesn't need to be super sharp that will quickly and abruptly create a wide cavity along the grain,this is called a splitting maul. It looks like a sledgehammer with a fat wedge on one side of the head.
For chopping you want a very sharp slender head that will cut across the grain and make a thin cut, like a knife blade, but not so heavy as to be difficult to wield horizontally to fell a tree. If you try to cut down a tree with a splitting maul you are just going to be crushing the wood fibers instead of cutting them. If you try to split with a chopping/felling axe you will need to put a lot more energy into the light weight head and it won't do a very good job of ripping the fibers apart to split the wood.
As mentioned before a chopping/felling axe, with the longest handle you can fit in the space available in your vehicle, would be best. Generally at camp for MOST of the year you are splitting small diameter logs that a chopping axe will do just fine and removing dead-fall across the trail. I would not want to try to cut a 12" diameter tree that fell across the trail with a splitting maul...it all boils down to what YOUR needs are.
Are you going to be removing dead-fall and small diameter dead trees and splitting them for a small camp fire? Use a chopping axe. I carry this in my truck all the time.
Are you wanting to split large diameter logs that were cut with a saw of one sort or another? Get a splitting maul. This I use a home for splitting wood cut with a chainsaw for filling my fireplace.
I have carried this for about 30 years, great quality for the price and has a solid steel shaft wrapped in a soft grip. It is a little short for any real chopping (I personally wouldn't get one shorter for any sort of two hand chopping) but since it fits perfectly where I want to store it in my truck and is quickly accessible no matter how full of gear my truck is I don't plan on getting another.
http://www.estwing.com/ao_campers_axe_long_handle.php
I wouldn't purchase an expensive axe to be used where there is a good chance you will hit rocks/dirt or be called upon for other uses for which it wasn't intended.
Keep the faces polished smooth and the axe blade sharp and life will be much easier.
A friend has a full size double blade axe that was purchased as a gift for him but due to it's size he doesn't leave it in the truck all of the time. It works much better than mine but....if you don't have it when you need it it does you no good.
Everyone has their own ideas of what is best for their uses, these are mine.
Darrell