After two rather wimpy Adventurers finding their death, one with a warhammer and the other as a striker/wrestler, my third was an axedwarf and has had great success. However, I'm not sure if it's because of the axe part, or just because he started with superior stats across the board except for memory and patience. He became a legendary wrestler in a blink of an eye as he cleared out a Giant family, because wrestle is all that Giants try to do, so he can loot the place and get a superior quality bronze great axe and just skip the shield because the crazy chopping power of the axe seemed so effective.
He's since become superdwarvenely in all the catagories he started as superior in, instantly enters a martial trance if there's a crowd of creatures, and if he doesn't instantly split something in half he severs all the limbs of the creature so fast it's incapacitated before it even can do anything. He's not even that skilled of an axedwarf
He couldn't hurt the bronze collosus but the collosus managed to charge and miss and fall off a cliff and die that way.
Like I said though it might just be the dwarf himself and not the axe, because he feels almost invincible. I also want to say something on wrestling though- after you grab someone, if you're strong enough when you throw them so they can fly and hit an obstacle, it seems to be quite sufficient at killing even those unkillable creatures.