Hi Kevin and everyone --back to my favorite topic!
Kevin--if you grasp (any) axe with your right hand the closest to the head of the axe, then it is official that you are right handed. You will feel comfortable using a Broadaxe with its handle gently swinging in towards your body, (this swing is away from the cutting edge or the flat of the axe.), also the log will be on your left hand side as you work along.
If in the above senario your left hand is the closest to the axe head then you are a left handed chopper, and everything is in reverse, for starters you will be hanging the handle from the opposite side of the head of the axe, but will swing out away from the flat of the blade. the log will always be on your right hand side as you work along.
The above instructions are for broadaxes that have their heads placed in the centre of the blades. The European heads generally would have to be either right or left handed models, so you would have to select one that suits you as an individual.
Some people can chop right or left handed and feel quite comfortable. My grandfather Michael who worked extensively in the lumber camps, could chop right or left handed but not many could.
Thanks for bringing this topic up it seems that from time to time it needs to be reviewed, and as noted above it may take a few tries before you actually have a properly curved handle that feels like it will be a keeper.
I personally like the feel of the antique handles for the chooping axes rather than just a straight handle. To me the swing in the body of the axe handle and the sharp bend at the end gives you more control, and you can place the cutting edge of the axe head to the exact angle of the cut, taking your height into account.
The only case of a straight handle being proper in my books is for a double bitted axe head, where you can flip it over and work with both cutting edges. These were used extensively in the lumber camps to help keep the choppers working steadier between sharpenings.