Here's a link to my blog post on the subject of axe handles and balance. I'd like to update it with a few additional notes and some minor structural revisions, but the core concept is there. It all sounds much more complicated than it really is, but once you understand the concept it becomes something that you can assess on an axe literally in a matter of seconds. I can even digitally design optimized handle templates for axes based on two good photos of an axe head (one in profile, and one from above to show the eye location) with the point of balance marked and the heel-to-toe measure of the bit for scale, without needing to ever lay hands on the head itself because the concept is so easily put to practical use.
However, on American axes, most heads are close enough to being balanced on their factory handles that the degree of offset in the neck of the handle is of minimal concern, and the curvature that seems to be in discussion here is mostly one regarding the butt end of the handle.
That question is the one that's particularly neither here nor there. How the axe is held and wielded is what determines how the presence or absence of a curve through the throat and knob will affect the stroke. Consider it as just giving you more options in how you
prefer to interface with the tool in your given context of use. The hang of the head, alignment of the bit, and the
length of the handle will have far more of an influence on how the axe is best delivered to the target than whether the gripped portion is straight or curved.
