Although an axe can be useful, I think that a decent bush saw is much more useful. Unless you want to fell a large tree or cut up a very wide log a saw will cut through most anything that is blocking your trail much faster than an axe.
Good points on the saw. Though I also use the backside of the head of my axe as a hammer. And it's a good emergency person extractor tool from a wreck. Honestly a lot of the emergency stuff I carry in my truck is for daily commuter wrecks. Never know if you'll be the first responder.
I carry an 18V sawsall with metal and wood cutting blades, pheumatic tools to run off my CO2 tank plus the normal wrenchs, sockets and drives. I also carry a replacement 1/2 shaft w/ cv's for the front in case one pops on the trail. :bigthumb: