My dad always liked his double bitted axe, which had a straight handle, this was necessary so you could turn it over to use the opposite side--his take was one side for chopping, and one side for trimming--both sharpened a little differently
he did have a one bitted or single bladed axe used exclusively for splitting firewood, this axe had a thicker blade which was necessary in the splitting action, and stronger along the edge to guard against hard knots and unusual twisting associated with wood splitting. this old axe to look at seemed pretty grim but man would it split wood!!!
the handle in this axe was hand made following a pattern that hung in the shop. it wasn't until I was involved more with wood working that I realized the importance of handles in general and how devastating it was to break one that you had become accustomed to. hanging a new handle needed many decisions such as not only the sweep of the handle but the angle of the cutting edge.
Creating and Installing a broken offset broad axe handle is one of the hardest jobs to do successfully, no matter how hard you try a new handle takes a lot of getting used to
Just the patina on the surface of the new wooden handle will feel strange and irritate your skin
The old handle that you became accustomed to made splitting the chalk line seem easy, slitting the line with the new handle will be aggravating and challenging to say the least