What do you plan to use the axe for? Cutting firewood? Clearing trail?
If it's for firewood then personally I like the combination of a good folding saw such as a Silky Big Boy 2000 and a splitting hatchet. The saw makes fast work of bucking logs, with less lost wood than an axe. It's also safer to use. In my area its easiest to find dry wood in the 2" to 8" diameter range so many pieces can go right on the fire, and a splitting hatchet can split up the bigger logs.
The Silky can also be used to clear trees up to about 8" diameter off the road. Anything larger than that and I'm not sure I'd want to try to cut through it with an axe (usually the tree is at an awkward height or angle), a chainsaw would be more useful, but I'd first try to just winch the tree to the side of the road.