Well, to comment from my woods experince cutting wood to build and heat my homes, as well as my extensive research, tomahawks were used as toolsto cut wood. They also make good weapons. They were the poor man's axe because they were easy to make as well as didn't use as much hard to get steel. A small sliver of good steel sanwiched between cheaper iron made a good cutter and was durable. Sailors used them on wooden ships for repairs and what you had to fight with when boarding parties came aboard. They were traded to native americans who took to them immediately. A good short history is available from David Grant in his book "Tomahawks- Traditional To Tactical"
I have litterally years working with axes and hatchets and find them usefull. If I have a choice, and I am in the woods etc. NOT working, then it is always one of my several tomahawks in solid steel. No wooden handles. Good ones are the same weight oddly enough as the wooden handle variety which I also own. Hard cutting or chopping of wood is always done with an axe. I hate hatchets. That is just me. Incidentally NONE of my tomahawks are convex....the edges on all I have ever seen are flat ground or concave.
Having a longer hawk handle does make it better for work but takes away its weapon advantage. You just can't manouver a long handle one handed in CQB. Don't ask me how I know this; I just do.
