Okay, so we have a guy with an oversized axe. The handle is basically a log, the blade that of a battleaxe but the size of a big-screen TV. To be more specific, the blade is big (wide/long) enough that it could cleave a tree trunk in two with a single blow. The 'axe dude' is strong enough that he can use the axe for this exact purpose, felling a tree with a single blow.
Thus we have Axe and Lumberjack. The Lumberjack can wield the battleaxe like a regular axe, despite its increased weight and size, and the axe is self-sharpening (is always razor-sharp, AKA the edge won't dull, blunt, or roll). In essence, we have a Really Good Blade (important for the question) and a typical physics-bending brute (a mere archetype).
My question is, In the Hands of Someone Strong Enough To Use It Properly, How Dangerous Would Such An Axe Be? In other words, with a super-strong man to use it, how dangerous would a giant axe with a remarkable edge be? Keep in mind, this axe can slice right through a tree with one blow....
Clarification:
The best answer will take into account what a giant axe would be used for (felling trees, chopping wood and/or stones, destroying an enemy knight, defeating a Savage)
Please assume that the ax user can wield the ax effectively despite its disproportionate weight and length.