The Long axe is, of course, a pole weapon and therefor shares some staff techniques. The axe blade itself will add chopping and slicing, mostly chopping. The shape of the head (of the weapon) can also add the possibility of hooking or spear techniques. These would be at a minimum of course. The main focus of the axe is attack. The defense is taken care of by the foot work since it is really difficult to stand in one place and swing the axe for any length of time anyway. The element of metal is obvious for the cutting but water is also a big component to the techniques. All five elements could be found so I will stop the comparison.
What the axe builds is Strength(duh), stances, footwork, and hand strength. It, along with hammer, will enhance the whole body as a unit concept and will build the back. It doesn't hit any specific muscle group. It works more as a unifying type of training as it uses the strength from Hammer and adds the precision required of a blade.
As for skills that transfer to open hand, in addition to the obvious weapon usage, axe will allow you to resist and counter most arm bars and throws. The blade skills will also increase your skill with arm bars and throws. The benefits to any grab/claw go without saying and Punching techniques that use twisting will also recieve a benefit.