Unless you are really weight size/restricted, the small two handed axes are much more versatile than the pure one handed ones. I would check the bit type vs local wood type, using one that is radically unoptomized can be similar to wearing winter clothes in the summer.
You generally want a different axe for cutting/felling and splitting, you can do either with the same axe, but if it does one of them well it will do the other fairly poorly. Bruks and Wetterling make solid axes in that size for both tasks, Wetterling is significantly cheaper.
Their patterns are basically hardwood profiles, but not heavily focused and work well over a broad range of woods but if your local wood is soft like pine you will want a thicker bit as they stick too bad, and if it is hard like spruce lumber they don't get enough penetration and need a deeper hollow and slimmer edge.
Fiskars and Roselli have better extreme softwood profiles, which also make them better splitters, I have not handled, or even seen better hardwood profiles, these are pretty rare now. The ones ones I have see are the ones people have made out of hand grinders.
Mete, now the vast majority of axes have a utility profile which is far more obtuse than anything used a few generations back. Hardware store axes have as much in common with wood working tools as a maul has to a finishing hammer.
-Cliff
